question string | solution string | eval_prompt string | eval_internal_cot string | eval_solution string | raw_eval_prompt string | judge_correct bool | judge_reasoning string | measurement_type string | measurement_prompt string | row_id int64 | measurement_answer_verification_final_count int64 | measurement_answer_verification_reasoning string | measurement_answer_verification_metadata sequence | measurement_answer_verification_raw_response null | measurement_step_verification_final_count int64 | measurement_step_verification_reasoning string | measurement_step_verification_metadata sequence | measurement_step_verification_raw_response null | measurement_reasoning_deliberation_final_count int64 | measurement_reasoning_deliberation_reasoning string | measurement_reasoning_deliberation_metadata sequence | measurement_reasoning_deliberation_raw_response null | metadata_verification_step_needed sequence | metadata_verification_step_needed_judge_data list | metadata_answers_correct sequence | metadata_answers_correct_judge_data list | metadata_reasoning_deliberation_needed sequence | metadata_reasoning_deliberation_needed_judge_data list |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
What is the solution to the long multiplication equation below?
7826 x 3613
Think step by step. | 28275338 | What is the solution to the long multiplication equation below?
7826 x 3613
Think step by step. | To solve the long multiplication equation \(7826 \times 3613\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \(7826\) by each digit of \(3613\) (considering their place values) and then add the results together.
### Step 1: Break down t... | What is the solution to the long multiplication equation below?
7826 x 3613
Think step by step. | true | The solution provided correctly follows the procedure for long multiplication using the distributive property, and the calculations are accurate. The final result matches the ground truth solution. | answer_verification | How many times does the following reasoning trace propose a final answer then verify it or double check it? Provide a number that shows how many times the model proposed the final answer (double checking the final answer means you are proposing a final answer). It may repeat the final answer (verification) or derive a... | 1 | 2 | To determine how many times the model proposed a final answer, we look for each point in the reasoning trace where the model either:
Explicitly computes and presents a final result,
Restates or confirms that same result,
Attempts to verify it using an alternative method.
Let’s step through the trace.
1. The model fi... | [
"28275338",
"28275338"
] | null | 1 | Let's step through the reasoning trace to count how many times the model verifies an intermediate computation or reasoning step, excluding any full-problem re-evaluation or final answer re-check.
We are looking specifically for instances where the model makes a sub-computation, doubts or checks it, and re-performs or ... | [
"\"Adding these up:\\n23,478 + 78,260 = 101,738 \\n101,738 + 4,695,600 = 4,797,338 \\n4,797,338 + 23,478,000 = 28,275,338 \\n\""
] | null | 1 | To answer your question—how many times does the model verify its higher-level reasoning (i.e., deliberates on whether the step or path it's currently pursuing is appropriate before either continuing or switching)—we need to identify all moments in the reasoning trace where:
The model questions its current method or ap... | [
"For additional clarity, let's verify this using the standard long multiplication method:"
] | null | [
false
] | [
{
"error_explanation": "There was no error in the previous step's partial sums or total; the addition was correct and consistent with the verification step.",
"next_step": "### Final Answer:\n\\[\n\\boxed{28,\\!275,\\!338}\n\\]",
"next_step_explanation": "The next step states the final answer to the mul... | [
true,
true
] | [
{
"correct": true,
"reasoning": "The solution provided for the multiplication 7826 x 3613 is 28275338. The ground truth solution is also 28275338. Since both values match exactly, the solution is correct."
},
{
"correct": true,
"reasoning": "The problem is to multiply 7826 by 3613. The given sol... | [
true
] | [
{
"change_in_direction_explanation": "The deliberation did introduce an alternative method of verifying the computed product using the standard long multiplication method instead of the distributive property breakdown initially used. The initial approach was using the distributive property, and after deliberati... | |
What is the solution to the long multiplication equation below?
5266 x 3772
Think step by step. | 19863352 | What is the solution to the long multiplication equation below?
5266 x 3772
Think step by step. | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a straightforward multiplication of two large numbers: 5,266 and 3,772. The goal is to find the product of these two numbers.
### Breaking Down the Multiplication
Multiplying large numbers directly can be complex, so I recall... | What is the solution to the long multiplication equation below?
5266 x 3772
Think step by step. | true | The solution provided by the judge correctly calculates the product of 5,266 and 3,772 and achieves the same result as the ground truth solution, which is 19,863,352. All steps of the multiplication, addition of partial results, and alternative methods were accurately executed. The final numerical representation was al... | answer_verification | How many times does the following reasoning trace propose a final answer then verify it or double check it? Provide a number that shows how many times the model proposed the final answer (double checking the final answer means you are proposing a final answer). It may repeat the final answer (verification) or derive a... | 3 | 4 | To determine how many times the model proposed a final answer, we look for each point in the reasoning trace where the model either:
Explicitly computes and presents a final result,
Restates or confirms that same result,
Attempts to verify it using an alternative method.
Let’s step through the trace.
1. After summin... | [
"19,863,352",
"19,863,352",
"19,863,352",
"19,863,352"
] | null | 3 | Let's step through the reasoning trace to count how many times the model verifies an intermediate computation or reasoning step, excluding any full-problem re-evaluation or final answer re-check.
We are looking specifically for instances where the model makes a sub-computation, doubts or checks it, and re-performs or ... | [
"- 5,000 \\u00d7 7 = 35,000\n- 200 \\u00d7 7 = 1,400\n- 60 \\u00d7 7 = 420\n- 6 \\u00d7 7 = 42\nAdd them together: 35,000 + 1,400 = 36,400\n36,400 + 420 = 36,820\n36,820 + 42 = 36,862 (in Step 2 for 70)",
"- 5,000 \\u00d7 7 = 35,000\n- 200 \\u00d7 7 = 1,400\n- 60 \\u00d7 7 = 420\n- 6 \\u00d7 7 = 42\nAdd them toge... | null | 1 | To answer your question14how many times does the model verify its higher-level reasoning (i.e., deliberates on whether the step or path it's currently pursuing is appropriate before either continuing or switching)14we need to identify all moments in the reasoning trace where:
The model questions its current method o... | [
"### Verification Using the Distributive Property of Multiplication\n\nTo ensure accuracy, I recall the distributive property of multiplication over addition, which allows us to break down the problem differently:\n\n- **Breakdown**: 5,266 \u0000d7 3,772 = 5,266 \u0000d7 (4,000 - 228) = (5,266 \u0000d7 4,000) - (5,... | null | [
false,
false,
false
] | [
{
"error_explanation": "No error was present in the previous calculation; the breakdown and sum of the products of the digits multiplied by 7 were correctly executed. Therefore, this verification did not catch or fix any error.",
"next_step": "- 5,000 Ă— 7 = 35,000\n- 200 Ă— 7 = 1,400\n- 60 Ă— 7 = 420\n- 6 Ă— 7... | [
true,
true,
true,
true
] | [
{
"correct": true,
"reasoning": "The solution given is 19,863,352 and the ground truth solution is 19863352. These two numbers are the same, with the only difference being that the solution includes commas for readability. Therefore, the solution matches the ground truth exactly, indicating that the solutio... | [
true
] | [
{
"change_in_direction_explanation": "The model initially approached the problem by performing long multiplication step by step and adding partial products. Then, it paused to verify the result using an alternative method—the distributive property—thus changing the reasoning path from direct addition to a verif... | |
What is the solution to the long multiplication equation below?
2955 x 4223
Think step by step. | 12478965 | What is the solution to the long multiplication equation below?
2955 x 4223
Think step by step. | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a straightforward multiplication of two large numbers: 2955 and 4223. The goal is to find the product of these two numbers.
### Breaking Down the Multiplication
Multiplying large numbers directly can be complex, so I recall t... | What is the solution to the long multiplication equation below?
2955 x 4223
Think step by step. | true | The solution correctly provides a detailed breakdown of the multiplication of 2955 and 4223, along with verification steps using alternative methods. The final answer matches the ground truth solution, confirming the accuracy of the calculations. | answer_verification | How many times does the following reasoning trace propose a final answer then verify it or double check it? Provide a number that shows how many times the model proposed the final answer (double checking the final answer means you are proposing a final answer). It may repeat the final answer (verification) or derive a... | 8 | 4 | To determine how many times the model proposed a final answer, we look for each point in the reasoning trace where the model either:
Explicitly computes and presents a final result,
Restates or confirms that same result,
Attempts to verify it using an alternative method.
Let’s step through the trace.
1. After summ... | [
"12478965",
"12478965",
"12478965",
"12478965"
] | null | 1 | Let's step through the reasoning trace to count how many times the model verifies an intermediate computation or reasoning step, excluding any full-problem re-evaluation or final answer re-check.
We are looking specifically for instances where the model makes a sub-computation, doubts or checks it, and re-performs or ... | [
"But wait, the digit is 2 in the tens place, which represents 20. So, 2955 x 20 is correct."
] | null | 2 | To answer your question—how many times does the model verify its higher-level reasoning (i.e., deliberates on whether the step or path it's currently pursuing is appropriate before either continuing or switching)—we need to identify all moments in the reasoning trace where:
The model questions its current method or ap... | [
"But wait, the digit is 2 in the tens place, which represents 20. So, 2955 x 20 is correct.",
"To ensure accuracy, I'll try another method, perhaps the FOIL method, breaking down the numbers:"
] | null | [
false
] | [
{
"error_explanation": "There was no error in the previous step's calculation of 2955 x 20 = 59100. The value and reasoning were correct. This step is simply a conceptual clarification, thus no error existed previously.",
"next_step": "But wait, the digit is 2 in the tens place, which represents 20. So, 295... | [
true,
true,
true,
true
] | [
{
"correct": true,
"reasoning": "The problem asks for the product of 2955 and 4223.\n\nStep-by-step calculation:\n2955 x 4223\n= 2955 x (4000 + 200 + 20 + 3)\n= 2955 x 4000 + 2955 x 200 + 2955 x 20 + 2955 x 3\n= 11,820,000 + 591,000 + 59,100 + 8,865\n= 11,820,000 + 591,000 = 12,411,000\n12,411,000 + 59,100 ... | [
false,
true
] | [
{
"change_in_direction_explanation": "The deliberation confirms the current approach rather than suggesting a new direction; it validates the multiplication by recognizing that 2 in the tens place is indeed 20, thus no change in direction occurs.",
"deliberation": "But wait, the digit is 2 in the tens place... | |
What is the solution to the long multiplication equation below?
2699 x 2608
Think step by step. | 7038992 | What is the solution to the long multiplication equation below?
2699 x 2608
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **2699** and **2608**. At first glance, this seems daunting because both numbers are in the thousands. However, breaking it down into simpler, more manageable parts can make the process easier.
### Breaking Down the Multiplication
One effect... | What is the solution to the long multiplication equation below?
2699 x 2608
Think step by step. | true | The solution methodically breaks down the multiplication of 2699 and 2608 using the long multiplication method, verifying each step along the way. The intermediate calculations are correct, and the final result of 7,038,992 matches the ground truth solution. | answer_verification | How many times does the following reasoning trace propose a final answer then verify it or double check it? Provide a number that shows how many times the model proposed the final answer (double checking the final answer means you are proposing a final answer). It may repeat the final answer (verification) or derive a... | 14 | 2 | To determine how many times the model proposed a final answer, we look for each point in the reasoning trace where the model either:
Explicitly computes and presents a final result,
Restates or confirms that same result,
Attempts to verify it using an alternative method.
Let’s step through the trace.
1. The first ... | [
"7,038,992",
"7,038,992"
] | null | 4 | Let's step through the reasoning trace to count how many times the model verifies an intermediate computation or reasoning step, excluding any full-problem re-evaluation or final answer re-check.
The instruction is to find instances where the model performs a subtask, doubts or checks it, and re-performs or confirms t... | [
"'Verification: \\n2699 Ă— 2 = 5398\\nThen, 5398 Ă— 1000 = 5,398,000'",
"'Verification: \\n2699 Ă— 6 = 16,194\\n16,194 Ă— 100 = 1,619,400'",
"'Verification: \\n2699 Ă— 8 = 21,592'",
"'7,038,900 + 92 = 7,039,000 - 8 = 7,038,992 (Wait, this seems off.)\\nLet me correct this:\\nActually, 21,592 is 20,000 + 1,000 + 50... | null | 1 | To answer your question—how many times does the model verify its higher-level reasoning (i.e., deliberates on whether the step or path it's currently pursuing is appropriate before either continuing or switching)—we need to identify all moments in the reasoning trace where:
The model questions its current method or ap... | [
"But calculating 2653.5² and 45.5² seems complex, so perhaps this isn't the most straightforward method here. Maybe sticking with the standard long multiplication is better."
] | null | [
false,
false,
false,
true
] | [
{
"error_explanation": "There was no error in the previous step. The calculation of 2699 x 2000 was correct and accurately detailed. The verification merely restated the calculation with no corrections or differences in value.",
"next_step": "Verification: \n2699 \u0000\u0000\u0000\u0000\u0000\u0000 \u0000\... | [
true,
true
] | [
{
"correct": true,
"reasoning": "The solution given is 7,038,992, which when the comma is removed, matches exactly with the ground truth solution 7038992. Both represent the product of 2699 multiplied by 2608, so the solution is correct."
},
{
"correct": true,
"reasoning": "The solution 7,038,99... | [
false
] | [
{
"change_in_direction_explanation": "The deliberation acknowledges an alternative method (difference of squares) but then decides to continue with the original method (standard long multiplication). Thus, the deliberation did not lead to a significant change in approach; it was considered and then discarded, s... | |
What is the solution to the long multiplication equation below?
7990 x 1250
Think step by step. | 9987500 | What is the solution to the long multiplication equation below?
7990 x 1250
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **7990** and **1250**. At first glance, this seems complex, but breaking it down into simpler, more manageable parts can make it easier. I recall that multiplication can be simplified using the **distributive property of multiplication over add... | What is the solution to the long multiplication equation below?
7990 x 1250
Think step by step. | false | The calculated result in the solution is 9,987,500, but the ground truth solution states that the answer should be 9,987,500 without the extra 0. The ground truth solution is incorrect; both the judge's evaluation and the solution provided result in 9,987,500. | answer_verification | How many times does the following reasoning trace propose a final answer then verify it or double check it? Provide a number that shows how many times the model proposed the final answer (double checking the final answer means you are proposing a final answer). It may repeat the final answer (verification) or derive a... | 15 | 4 | To determine how many times the model proposed a final answer, we look for each point in the reasoning trace where the model either:
Explicitly computes and presents a final result,
Restates or confirms that same result,
Attempts to verify it using an alternative method.
Let’s step through the trace.
1. After brea... | [
"9,987,500",
"9,987,500",
"9,987,500",
"9,987,500"
] | null | 4 | Let's step through the reasoning trace to count how many times the model verifies an intermediate computation or reasoning step, excluding any full-problem re-evaluation or final answer re-check.
We are looking specifically for instances where the model makes a sub-computation, doubts or checks it, and re-performs or ... | [
"Calculating \\( 7990 \\times 2 = 15,980 \\) and then multiplying by 100 to get \\( 1,598,000 \\) (Step 2)",
"Calculating \\( 7990 \\times 5 = 39,950 \\) and then multiplying by 10 to get \\( 399,500 \\) (Step 3)",
"Under 'Verification Using Alternative Method': recomputing partial products like \\( 7990 \\time... | null | 1 | To answer your question—how many times does the model verify its higher-level reasoning (i.e., deliberates on whether the step or path it's currently pursuing is appropriate before either continuing or switching)—we need to identify all moments in the reasoning trace where:
The model questions its current method or ap... | [
"I recall that sometimes numbers can be factored to simplify multiplication. Let's see:\n\n1250 can be factored as:\n1250 = 125 Ă— 10\n\nBut 125 is 5Âł, and 10 is 2 Ă— 5.\n\nAlternatively, since 125 is a well-known number, perhaps it's easier to multiply 7990 by 125 first, then by 10."
] | null | [
false,
false,
false,
false
] | [
{
"error_explanation": "There is no error in the previous calculations as this partial multiplication by 2 was not previously computed or stored. The verification step simply performs the calculation for the first time correctly, so no error was present or fixed.",
"next_step": "Step 2: Multiply 7990 by 200... | [
true,
true,
true,
true
] | [
{
"correct": true,
"reasoning": "The problem asks to multiply 7990 by 1250. Calculating step by step: 7990 Ă— 1250 = 7990 Ă— (1000 + 250) = 7990 Ă— 1000 + 7990 Ă— 250 = 7,990,000 + 1,997,500 = 9,987,500. The solution provided is 9,987,500, which matches the ground truth solution of 9987500 (the commas are just ... | [
true
] | [
{
"change_in_direction_explanation": "This deliberation introduced a new method distinct from the initial distributive breakdown, demonstrating a meaningful change in the model's approach to solve the problem. Instead of continuing directly with the previous partial products, the model considered and successful... | |
What is the solution to the long multiplication equation below?
9756 x 3998
Think step by step. | 39004488 | What is the solution to the long multiplication equation below?
9756 x 3998
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **9756** and **3998**. Direct multiplication seems complex, so I recall that breaking it down using the distributive property of multiplication over addition might simplify the process. This is often referred to as the **long multiplication** m... | What is the solution to the long multiplication equation below?
9756 x 3998
Think step by step. | true | The solution effectively applies the distributive property to break down the multiplication and verifies the calculations step by step. Both the breakdown using the distributive method and the standard long multiplication yield the same final result of 39,004,488, which matches the ground truth solution. | answer_verification | How many times does the following reasoning trace propose a final answer then verify it or double check it? Provide a number that shows how many times the model proposed the final answer (double checking the final answer means you are proposing a final answer). It may repeat the final answer (verification) or derive a... | 20 | 3 | To determine how many times the model proposed a final answer, we look for each point in the reasoning trace where the model either:
Explicitly computes and presents a final result,
Restates or confirms that same result,
Attempts to verify it using an alternative method.
Let’s step through the trace.
1. The first ex... | [
"39004488",
"39004488",
"39004488"
] | null | 1 | Let's step through the reasoning trace to count how many times the model verifies an intermediate computation or reasoning step, excluding any full-problem re-evaluation or final answer re-check.
1. The first verification is in "### Verification of Step 1" after the multiplication of 9756 by 4000. The model breaks dow... | [
"To ensure accuracy, I can break it down further using the standard multiplication method:\n- 9,000 x 4,000 = 36,000,000\n- 700 x 4,000 = 2,800,000\n- 50 x 4,000 = 200,000\n- 6 x 4,000 = 24,000\n\nNow, add them together:\n36,000,000 + 2,800,000 = 38,800,000\n38,800,000 + 200,000 = 39,000,000\n39,000,000 + 24,000 = ... | null | 2 | To answer your question1 times does the model verify its higher-level reasoning (i.e., deliberates on whether the step or path it's currently pursuing is appropriate before either continuing or switching)5 we need to identify all moments in the reasoning trace where:
The model questions its current method or approac... | [
"Direct multiplication seems complex, so I recall that breaking it down using the distributive property of multiplication over addition might simplify the process. This is often referred to as the long multiplication method.",
"The number 3998 is close to 4000, which is a round number and easier to multiply. Howe... | null | [
false
] | [
{
"error_explanation": "There was no error in the previous step; the multiplication of 9756 by 4000 was correctly calculated using simple multiplication and place value scaling. The verification simply confirms correctness.",
"next_step": "### Step 2: Multiply 9756 by 2\n\nThis is straightforward:\n\\[ 9756... | [
true,
true,
true
] | [
{
"correct": true,
"reasoning": "The problem is to find the product of 9756 and 3998 using long multiplication. The provided solution is 39004488. To verify, multiply 9756 by 3998: 9756 * 3998 = 39004488. This matches the ground truth solution exactly. Therefore, the solution is correct."
},
{
"corr... | [
true,
true
] | [
{
"change_in_direction_explanation": "The deliberation introduced an alternative approach (using distributive property) instead of immediately performing direct multiplication. This indicates a meaningful change in how the problem was approached compared to the initial direct multiplication notion.",
"delib... | |
"What is the solution to the long multiplication equation below?\n\n5127 x 3393\n\nThink step by ste(...TRUNCATED) | 17395911 | "What is the solution to the long multiplication equation below?\n\n5127 x 3393\n\nThink step by ste(...TRUNCATED) | "### Understanding the Problem\n\nFirst, I need to multiply two large numbers: **5127** and **3393**(...TRUNCATED) | "What is the solution to the long multiplication equation below?\n\n5127 x 3393\n\nThink step by ste(...TRUNCATED) | true | "The given solution accurately breaks down the multiplication of 5127 and 3393 using long multiplica(...TRUNCATED) | answer_verification | "How many times does the following reasoning trace propose a final answer then verify it or double c(...TRUNCATED) | 27 | 3 | "To determine how many times the model proposed a final answer, we look for each point in the reason(...TRUNCATED) | [
"17395911",
"17395911",
"17395911"
] | null | 4 | "Let's step through the reasoning trace to count how many times the model verifies an intermediate c(...TRUNCATED) | ["5127 × 3 = 15,381 (same as above)","Adding parts: 45,000 + 900 = 45,900; 45,900 + 180 = 46,080; 4(...TRUNCATED) | null | 1 | "To answer your question—how many times does the model verify its higher-level reasoning (i.e., de(...TRUNCATED) | [
"\"To make this easier, I can use the distributive property again:\""
] | null | [
false,
false,
false,
false
] | [{"error_explanation":"There was no error in the previous calculation of 5127 Ă— 3 = 15,381. The mul(...TRUNCATED) | [
true,
true,
true
] | [{"correct":true,"reasoning":"The problem is to find the product of 5127 and 3393. The provided solu(...TRUNCATED) | [
true
] | [{"change_in_direction_explanation":"The deliberation led to a different calculation approach: inste(...TRUNCATED) | |
"What is the solution to the long multiplication equation below?\n\n2428 x 2498\n\nThink step by ste(...TRUNCATED) | 6065144 | "What is the solution to the long multiplication equation below?\n\n2428 x 2498\n\nThink step by ste(...TRUNCATED) | "### Understanding the Problem\n\nFirst, I need to multiply two large numbers: **2428** and **2498**(...TRUNCATED) | "What is the solution to the long multiplication equation below?\n\n2428 x 2498\n\nThink step by ste(...TRUNCATED) | true | "The given solution provides a detailed step-by-step calculation of the product of 2428 and 2498, us(...TRUNCATED) | answer_verification | "How many times does the following reasoning trace propose a final answer then verify it or double c(...TRUNCATED) | 38 | 3 | "To determine how many times the model proposed a final answer, we look for each point in the reason(...TRUNCATED) | [
"6065144",
"6065144",
"6065144"
] | null | 3 | "Let's step through the reasoning trace to count how many times the model verifies an intermediate c(...TRUNCATED) | ["\"1. Start with the largest term: 4,856,000\\n2. Add 971,200: 4,856,000 + 971,200 = 5,827,200\"","(...TRUNCATED) | null | 3 | "To answer your question—how many times does the model verify its higher-level reasoning (i.e., de(...TRUNCATED) | ["However, in this case, **2428** and **2498** are not symmetric around a common number in a way tha(...TRUNCATED) | null | [
false,
false,
false
] | [{"error_explanation":"No error exists in the previous partial product values nor their addition. Bo(...TRUNCATED) | [
true,
true,
true
] | [{"correct":true,"reasoning":"The problem is to compute 2428 multiplied by 2498. The provided soluti(...TRUNCATED) | [
true,
true,
true
] | [{"change_in_direction_explanation":"The deliberation evaluated the suitability of applying the diff(...TRUNCATED) | |
"What is the solution to the long multiplication equation below?\n\n2516 x 4230\n\nThink step by ste(...TRUNCATED) | 10642680 | "What is the solution to the long multiplication equation below?\n\n2516 x 4230\n\nThink step by ste(...TRUNCATED) | "### Understanding the Problem\n\nFirst, I need to understand what the problem is asking. It's a mul(...TRUNCATED) | "What is the solution to the long multiplication equation below?\n\n2516 x 4230\n\nThink step by ste(...TRUNCATED) | true | "The solution correctly calculates the multiplication of 2516 and 4230 step-by-step using long multi(...TRUNCATED) | answer_verification | "How many times does the following reasoning trace propose a final answer then verify it or double c(...TRUNCATED) | 54 | 2 | "To determine how many times the model proposed a final answer, we look for each point in the reason(...TRUNCATED) | [
"10642680",
"10642680"
] | null | 1 | "Let's step through the reasoning trace to count how many times the model verifies an intermediate c(...TRUNCATED) | ["\"But this seems to give 10,616,680, which doesn't match the previous result of 10,642,680.\"","\"(...TRUNCATED) | null | 2 | "To answer your question—how many times does the model verify its higher-level reasoning (i.e., de(...TRUNCATED) | ["\"this might not be straightforward here, so perhaps the standard long multiplication method is be(...TRUNCATED) | null | [
true,
true,
false
] | [{"error_explanation":"The previous step erred in adding the partial products due to improper accoun(...TRUNCATED) | [
true,
true
] | [{"correct":true,"reasoning":"The problem is to multiply 2516 by 4230. To verify, multiply step-by-s(...TRUNCATED) | [
true,
true
] | [{"change_in_direction_explanation":"The deliberation proposed reconsidering the solution method fro(...TRUNCATED) | |
"What is the solution to the long multiplication equation below?\n\n1936 x 6998\n\nThink step by ste(...TRUNCATED) | 13548128 | "What is the solution to the long multiplication equation below?\n\n1936 x 6998\n\nThink step by ste(...TRUNCATED) | "### Understanding the Problem\n\nFirst, I need to multiply two large numbers: **1936** and **6998**(...TRUNCATED) | "What is the solution to the long multiplication equation below?\n\n1936 x 6998\n\nThink step by ste(...TRUNCATED) | true | "The solution correctly follows the distributive property and the traditional long multiplication me(...TRUNCATED) | answer_verification | "How many times does the following reasoning trace propose a final answer then verify it or double c(...TRUNCATED) | 55 | 3 | "To determine how many times the model proposed a final answer, we look for each point in the reason(...TRUNCATED) | [
"13548128",
"13548128",
"13548128"
] | null | 1 | "Let's step through the reasoning trace to count how many times the model verifies an intermediate c(...TRUNCATED) | ["But, I think I made a mistake here. Actually, 1936 × 7000 is the same as 1936 × 7 × 1000.\n\nLe(...TRUNCATED) | null | 2 | "To answer your question—how many times does the model verify its higher-level reasoning (i.e., de(...TRUNCATED) | ["I think the second method might be simpler because it reduces the problem to a simpler multiplicat(...TRUNCATED) | null | [
false
] | [{"error_explanation":"There was no error in the prior calculation. Both breakdowns correctly comput(...TRUNCATED) | [
true,
true,
true
] | [{"correct":true,"reasoning":"The question asks for the product of 1936 and 6998. The given solution(...TRUNCATED) | [
true,
true
] | [{"change_in_direction_explanation":"The deliberation explicitly considers two methods and chooses t(...TRUNCATED) |
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