You will receive a question-answer pair. Your task is to:

1. Decompose the answer into a sequence of numbered steps ("Step 1", "Step 2", etc.).
2. For each step, include a reasoning description and assign a confidence score (a float between 0 and 1).
3. For accepted answers, ensure reasoning steps are correct, with confidence scores that progressively increase as the steps approach the final answer.
4. For rejected answers, introduce flaws or errors in reasoning steps, and use inconsistent or lower confidence scores.   the text content itself.

### Suggested JSON Structure

{
  "prompt": "Question text here",
  "responses": [
    {
      "content": "Step 1: Calculate the production rate of each printer (confidence: 0.7)\nStep 2: Find how many documents one printer can produce (confidence: 0.8)\nStep 3: Divide 75 by the production rate to get 15 printers (confidence: 0.9)",
      "type": "accepted"
    },
    {
      "content": "Step 1: Miscalculate the production rate (confidence: 0.4)\nStep 2: Incorrectly assume one printer produces 15 documents per minute (confidence: 0.3)\nStep 3: Conclude only 5 printers are needed (confidence: 0.2)",
      "type": "rejected"
    }
  ]
}

### Updated Prompt Example

---

Prompt Example:

plaintext
You will receive a question-answer pair. Your task is to:

1. For the *accepted answer*, decompose the reasoning into steps (Step 1, Step 2, etc.) and write a confidence score for each step in parentheses.
2. For the *rejected answer*, introduce flawed reasoning steps and inconsistent or lower confidence scores.

Please output your response in JSON format, with the question in a "prompt" field and the two answers in a "responses" list. Each answer should include:
   - "content": containing the answer reasoning in steps with confidence scores in parentheses after each step.
   - "type": with either "accepted" or "rejected".

---

*Example Output:*

```json
{
  "prompt": "Sample question text",
  "responses": [
    {
      "content": "Step 1: Identify human activities (confidence: 0.7)\nStep 2: Specify fossil fuel burning as a cause (confidence: 0.8)\nStep 3: Explain deforestation effects (confidence: 0.9)",
      "type": "accepted"
    },
    {
      "content": "Step 1: Incorrectly focus on natural factors (confidence: 0.5)\nStep 2: Mention volcanic activity inaccurately (confidence: 0.3)\nStep 3: Avoid specifics on human activities (confidence: 0.4)",
      "type": "rejected"
    }
  ]
}

Question: A certain five-digit integer $A\,B\,C\,D\,E$, where each letter represents a digit, has the property that when divided by $7$, it leaves a remainder of $2$, but when divided by $11$, it leaves a remainder of $3$. Furthermore, $C$ is exactly twice the value of $B$, and the sum of the digits $A + B + D + E = 17$. Determine the largest possible value of $C$.

(Note: I've tried to create a problem that requires a different approach to solve, using modular arithmetic and the properties of divisibility, rather than just relying on the sum of digits as in the original problem.)
Answer: ## Step 1: Understand the conditions given for the five-digit integer
We are given a five-digit integer $A\,B\,C\,D\,E$ with specific properties: it leaves a remainder of 2 when divided by 7, and a remainder of 3 when divided by 11. Additionally, $C$ is exactly twice the value of $B$, and the sum of the digits $A + B + D + E = 17$.

## Step 2: Express the conditions using modular arithmetic
From the given conditions, we can express the five-digit integer in terms of modular arithmetic. For the remainder when divided by 7, we have $A\,B\,C\,D\,E \equiv 2 \pmod{7}$. For the remainder when divided by 11, we have $A\,B\,C\,D\,E \equiv 3 \pmod{11}$.

## Step 3: Use the divisibility rule for 11 to express the alternating sum of digits
The divisibility rule for 11 states that a number is divisible by 11 if the alternating sum of its digits is divisible by 11. Applying this to our number, we have $A - B + C - D + E \equiv 3 \pmod{11}$.

## Step 4: Consider the relationship between B and C
We know that $C$ is exactly twice the value of $B$, so we can express $C$ as $C = 2B$.

## Step 5: Substitute C = 2B into the alternating sum of digits
Substituting $C = 2B$ into the alternating sum, we get $A - B + 2B - D + E \equiv 3 \pmod{11}$, which simplifies to $A + B - D + E \equiv 3 \pmod{11}$.

## Step 6: Use the given sum of digits to relate A, B, D, and E
We are given that $A + B + D + E = 17$. We can use this information to find a relationship between $A, B, D,$ and $E$.

## Step 7: Find the largest possible value of C
To find the largest possible value of $C$, we need to consider the possible values of $B$ and the constraints imposed by the given conditions.

## Step 8: Analyze the constraints on B and C
Since $C$ is twice the value of $B$, the largest possible value of $C$ will depend on the largest possible value of $B$. We need to analyze the constraints on $B$ and $C$ to determine their largest possible values.

## Step 9: Determine the largest possible value of B
Considering the constraints imposed by the given conditions, we can determine the largest possible value of $B$.

## Step 10: Calculate the largest possible value of C
Once we have the largest possible value of $B$, we can calculate the largest possible value of $C$ using the relationship $C = 2B$.

The final answer is: $\boxed{8}$