ProblemIdx int64 3 918 | SystemPrompt stringclasses 5
values | UserPrompt stringlengths 63 73.4k | ExpectedOutput stringlengths 47 45.8k | FinalAnswer stringlengths 1 51 | Phase float64 1 12 | __index_level_0__ int64 5 7.09k | messages listlengths 3 3 |
|---|---|---|---|---|---|---|---|
3 | You are the planner of an AI system that follows a systematic long thinking process to arrive at the precise and accurate answer to a math question specified within <Question> and </Question> tags. The system consists of a planner and multiple executors that can run in parallel. The solution is generated over multiple ... | <Question>
Let $m$ be a constant not equal to $0$ or $1.$ Then the graph of \[x^2 + my^2 = 4\]is a conic section with two foci. Find all values of $m$ such that the foci both lie on the circle $x^2+y^2=16.$
Enter all possible values of $m,$ separated by commas.
</Question>
<Plan_1>
Okay, so I need to find all values ... | <Plan_3>
Based on execution_2.1:
Wait, this is getting a bit confusing. Let me take it step by step.
Case 1: m > 0. Then the equation x² + my² = 4 is an ellipse.
<prompt> Calculate the foci of the ellipse for m > 0 and verify if they lie on the circle x² + y² = 16. </prompt>
Based on execution_2.2:
Case 2: m < 0. Th... | \frac{1}{5}, -\frac{1}{3} | 3 | 5 | [
{
"content": "You are the planner of an AI system that follows a systematic long thinking process to arrive at the precise and accurate answer to a math question specified within <Question> and </Question> tags. The system consists of a planner and multiple executors that can run in parallel. The solution is ge... |
3 | You are the planner of an AI system that follows a systematic long thinking process to arrive at the precise and accurate answer to a math question specified within <Question> and </Question> tags. The system consists of a planner and multiple executors that can run in parallel. The solution is generated over multiple ... | <Question>
Let $m$ be a constant not equal to $0$ or $1.$ Then the graph of \[x^2 + my^2 = 4\]is a conic section with two foci. Find all values of $m$ such that the foci both lie on the circle $x^2+y^2=16.$
Enter all possible values of $m,$ separated by commas.
</Question>
<Plan_1>
Okay, so I need to find all values ... | <Plan_4>
Based on execution_3.2:
But wait, let me check if this is correct. Let me verify the steps again.
For the hyperbola case, when m is negative, we have the equation x² + my² = 4. Let's write m as -k where k > 0.
<prompt> Verify and correct the calculation of the foci for the hyperbola when m < 0. </prompt>
---... | \frac{1}{5}, -\frac{1}{3} | 4 | 9 | [
{
"content": "You are the planner of an AI system that follows a systematic long thinking process to arrive at the precise and accurate answer to a math question specified within <Question> and </Question> tags. The system consists of a planner and multiple executors that can run in parallel. The solution is ge... |
3 | You are the planner of an AI system that follows a systematic long thinking process to arrive at the precise and accurate answer to a math question specified within <Question> and </Question> tags. The system consists of a planner and multiple executors that can run in parallel. The solution is generated over multiple ... | <Question>
Let $m$ be a constant not equal to $0$ or $1.$ Then the graph of \[x^2 + my^2 = 4\]is a conic section with two foci. Find all values of $m$ such that the foci both lie on the circle $x^2+y^2=16.$
Enter all possible values of $m,$ separated by commas.
</Question>
<Plan_1>
Okay, so I need to find all values ... | <Plan_7>
Based on execution_6.1, execution_3.3:
Therefore, the possible values of m are 1/5 and -1/3.
Wait, let me confirm this. Let's check m = 1/5.
<prompt> Confirm all possible solutions by verifying the calculations for both m = 1/5 and m = -1/3. </prompt>
</Plan_7> | \frac{1}{5}, -\frac{1}{3} | 7 | 18 | [
{
"content": "You are the planner of an AI system that follows a systematic long thinking process to arrive at the precise and accurate answer to a math question specified within <Question> and </Question> tags. The system consists of a planner and multiple executors that can run in parallel. The solution is ge... |
3 | You are the planner of an AI system that follows a systematic long thinking process to arrive at the precise and accurate answer to a math question specified within <Question> and </Question> tags. The system consists of a planner and multiple executors that can run in parallel. The solution is generated over multiple ... | <Question>
Let $m$ be a constant not equal to $0$ or $1.$ Then the graph of \[x^2 + my^2 = 4\]is a conic section with two foci. Find all values of $m$ such that the foci both lie on the circle $x^2+y^2=16.$
Enter all possible values of $m,$ separated by commas.
</Question>
<Plan_1>
Okay, so I need to find all values ... | <Final_answer>
Therefore, the possible values of $m$ are $m = \boxed{\frac{1}{5}, -\frac{1}{3}}.
$
</Final_answer> | \frac{1}{5}, -\frac{1}{3} | 8 | 20 | [
{
"content": "You are the planner of an AI system that follows a systematic long thinking process to arrive at the precise and accurate answer to a math question specified within <Question> and </Question> tags. The system consists of a planner and multiple executors that can run in parallel. The solution is ge... |
4 | You are the planner of an AI system that follows a systematic long thinking process to arrive at the precise and accurate answer to a math question specified within <Question> and </Question> tags. The system consists of a planner and multiple executors that can run in parallel. The solution is generated over multiple ... | <Question>
Let $m$ be a constant not equal to $0$ or $1.$ Then the graph of \[x^2 + my^2 = 4\]is a conic section with two foci. Find all values of $m$ such that the foci both lie on the circle $x^2+y^2=16.$
Enter all possible values of $m,$ separated by commas.
</Question>
<Plan_1>
Okay, so I need to find all values ... | <Plan_5>
Based on execution_4.2, execution_4.3:
Therefore, this is the only solution.
Therefore, the only value of m is -1/3. So, the answer should be \boxed{-\dfrac{1}{3}}.
<prompt> Perform a final verification and conclude the possible values of m. </prompt>
</Plan_5> | \frac{1}{5}, -\frac{1}{3} | 5 | 34 | [
{
"content": "You are the planner of an AI system that follows a systematic long thinking process to arrive at the precise and accurate answer to a math question specified within <Question> and </Question> tags. The system consists of a planner and multiple executors that can run in parallel. The solution is ge... |
4 | "You are the planner of an AI system that follows a systematic long thinking process to arrive at th(...TRUNCATED) | "<Question>\nLet $m$ be a constant not equal to $0$ or $1.$ Then the graph of \\[x^2 + my^2 = 4\\]is(...TRUNCATED) | "<Final_answer>\nTherefore, the possible values of $m$ are $m = \\boxed{\\frac{1}{5}, -\\frac{1}{3}}(...TRUNCATED) | \frac{1}{5}, -\frac{1}{3} | 6 | 36 | [{"content":"You are the planner of an AI system that follows a systematic long thinking process to (...TRUNCATED) |
6 | "You are the planner of an AI system that follows a systematic long thinking process to arrive at th(...TRUNCATED) | "<Question>\nThe real number $x$ satisfies\n\\[3x + \\frac{1}{2x} = 3.\\]Find\n\\[64x^6 + \\frac{1}{(...TRUNCATED) | <Final_answer>
&= \boxed{\frac{416}{27}}.
\end{align*}
</Final_answer> | \frac{416}{27} | 11 | 67 | [{"content":"You are the planner of an AI system that follows a systematic long thinking process to (...TRUNCATED) |
17 | "You are the planner of an AI system that follows a systematic long thinking process to arrive at th(...TRUNCATED) | "<Question>\nA street has 50 houses on each side, for a total of 100 houses. The addresses on the so(...TRUNCATED) | "<Plan_7>\nBased on execution_6.1:\nSo for the south side: addresses are 1,5,9,13,...., 4*50 -3 = 19(...TRUNCATED) | 245 | 7 | 88 | [{"content":"You are the planner of an AI system that follows a systematic long thinking process to (...TRUNCATED) |
17 | "You are the planner of an AI system that follows a systematic long thinking process to arrive at th(...TRUNCATED) | "<Question>\nA street has 50 houses on each side, for a total of 100 houses. The addresses on the so(...TRUNCATED) | "<Plan_8>\nBased on execution_7.1:\nWait, but wait. Let me verify the number of terms:\n\n<prompt> V(...TRUNCATED) | 245 | 8 | 90 | [{"content":"You are the planner of an AI system that follows a systematic long thinking process to (...TRUNCATED) |
17 | "You are the planner of an AI system that follows a systematic long thinking process to arrive at th(...TRUNCATED) | "<Question>\nA street has 50 houses on each side, for a total of 100 houses. The addresses on the so(...TRUNCATED) | "<Final_answer>\nThus, the total revenue is $1\\times5 + 2\\times 45 + 3\\times 50 = \\boxed{245}$.\(...TRUNCATED) | 245 | 9 | 92 | [{"content":"You are the planner of an AI system that follows a systematic long thinking process to (...TRUNCATED) |
End of preview. Expand in Data Studio
README.md exists but content is empty.
- Downloads last month
- 14