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: Find the median of all solutions for $y$ when $y^4 - 2y^3 - 5y^2 = 0$.
Answer: To find the median of all solutions for $y$ when $y^4 - 2y^3 - 5y^2 = 0$, first, factor out $y^2$ from the equation:
\[ y^2 (y^2 - 2y - 5) = 0 \]

This gives us two separate equations to solve:
1. $y^2 = 0$
2. $y^2 - 2y - 5 = 0$

For the first equation, the solution is straightforward:
\[ y^2 = 0 \Rightarrow y = 0 \]

For the second equation, use the quadratic formula where $a = 1$, $b = -2$, and $c = -5$:
\[ y = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]

Substitute $a$, $b$, and $c$ into the formula:
\[ y = \frac{-(-2) \pm \sqrt{(-2)^2 - 4(1)(-5)}}{2(1)} \]
\[ y = \frac{2 \pm \sqrt{4 + 20}}{2} \]
\[ y = \frac{2 \pm \sqrt{24}}{2} \]
\[ y = \frac{2 \pm 2\sqrt{6}}{2} \]
\[ y = 1 \pm \sqrt{6} \]

So, the solutions for $y$ are $0$, $1 + \sqrt{6}$, and $1 - \sqrt{6}$.

To find the median, we need to arrange these solutions in ascending order:
\[ 1 - \sqrt{6}, 0, 1 + \sqrt{6} \]

Since there are three solutions (an odd number), the median is the middle value, which is $0$.

Therefore, the median of all solutions for $y$ is:
\[ \boxed{0} \]