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: The equation $\frac{x-3}{x+5} = \frac{y-2}{y-7}$ is equivalent to the equation $ax+by+c=0$, where $a, b, c$ are nonzero constants. Find $a+b+c$.
Answer: The given equation is
\[ \frac{x - 3}{x + 5} = \frac{y - 2}{y - 7} \]

Cross-multiply to eliminate the fractions:
\[ (x - 3)(y - 7) = (x + 5)(y - 2) \]

Expand both sides:
\[ xy - 7x - 3y + 21 = xy - 2x + 5y - 10 \]

Simplify and rearrange terms:
\[ -7x - 3y + 21 = -2x + 5y - 10 \]

Move all terms to one side to set the equation to 0:
\[ -7x - 3y + 21 + 2x - 5y + 10 = 0 \]

Combine like terms:
\[ -5x - 8y + 31 = 0 \]

Now we have the equation in the form $ax + by + c = 0$.

Comparing, we find that $a = -5$, $b = -8$, and $c = 31$.

Thus, $a + b + c = -5 - 8 + 31 = \boxed{18}$