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.

Please output the response in the JSON format below, following the example provided.


---

*Expected JSON Output Format:*

{
  "question": "[Insert question text here]",
  "accepted_answer": {
    "Step 1": {
      "reasoning": "[Describe the first reasoning step here]",
      "confidence_score": [Float between 0 and 1, e.g., 0.7]
    },
    "Step 2": {
      "reasoning": "[Describe the next reasoning step]",
      "confidence_score": [Incrementally higher float, e.g., 0.8]
    },
    "Step 3": {
      "reasoning": "[Continue describing each step with incrementally higher scores]",
      "confidence_score": [Approaching 1, e.g., 0.9]
    }
    // Continue until the final reasoning step
  },
  "rejected_answer": {
    "Step 1": {
      "reasoning": "[Introduce an incorrect or misleading reasoning step here]",
      "confidence_score": [Lower or inconsistent float, e.g., 0.5]
    },
    "Step 2": {
      "reasoning": "[Add a flawed or irrelevant reasoning step]",
      "confidence_score": [Inconsistent or lower float, e.g., 0.4]
    },
    "Step 3": {
      "reasoning": "[Continue with errors or inconsistencies in reasoning]",
      "confidence_score": [Non-incremental or lower float, e.g., 0.6]
    }
    // Continue until the final flawed reasoning step
  }
}

---

*Example JSON Output:*

{
  "question": "What are the primary causes of climate change?",
  "accepted_answer": {
    "Step 1": {
      "reasoning": "Identify human activities as significant contributors to climate change.",
      "confidence_score": 0.7
    },
    "Step 2": {
      "reasoning": "Specify fossil fuel burning as a major source of greenhouse gases.",
      "confidence_score": 0.8
    },
    "Step 3": {
      "reasoning": "Explain how deforestation reduces CO2 absorption, increasing atmospheric CO2.",
      "confidence_score": 0.9
    }
  },
  "rejected_answer": {
    "Step 1": {
      "reasoning": "Suggest natural factors as primary contributors to climate change.",
      "confidence_score": 0.5
    },
    "Step 2": {
      "reasoning": "Mention volcanic activity as a significant greenhouse gas source, incorrect for recent climate trends.",
      "confidence_score": 0.4
    },
    "Step 3": {
      "reasoning": "Briefly describe human activities without identifying specific sources.",
      "confidence_score": 0.6
    }
  }
}

Question: Two circles have radii $r_1$ and $r_2$ respectively. The sum of their areas is $16\pi$ and the difference of their circumferences is $4\pi$. What is the positive difference between the radii of the two circles?
Answer: We know that the area of a circle is $\pi r^2$ and the circumference is $2\pi r$.

Given:
\[ \pi r_1^2 + \pi r_2^2 = 16\pi \Rightarrow r_1^2 + r_2^2 = 16 \quad (1) \]

\[ 2\pi r_1 - 2\pi r_2 = 4\pi \Rightarrow r_1 - r_2 = 2 \quad (2) \]

Solve for $r_1$ and $r_2$.

From (2), we have $r_1 = r_2 + 2$.

Substitute $r_1 = r_2 + 2$ into (1):
\[ (r_2 + 2)^2 + r_2^2 = 16 \Rightarrow r_2^2 + 4r_2 + 4 + r_2^2 = 16 \Rightarrow 2r_2^2 + 4r_2 - 12 = 0 \]

\[ r_2^2 + 2r_2 - 6 = 0 \Rightarrow (r_2 + 3)(r_2 - 2) = 0 \Rightarrow r_2 = -3 \text{ or } r_2 = 2 \]

Since $r_2$ is a radius, it cannot be negative. Therefore, $r_2 = 2$.

Now, find $r_1$:
\[ r_1 = r_2 + 2 = 2 + 2 = 4 \]

The positive difference between the radii is:
\[ r_1 - r_2 = 4 - 2 = \boxed{2} \]