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: In triangle $PQR$, the angle bisectors of $\angle P$ and $\angle Q$ intersect at $S$ and have lengths $8$ and $10$, respectively. Let $T$ be the intersection point of the angle bisector of $\angle R$ with the circumcircle of triangle $PQR$. Find the distance between $S$ and $T$.
Answer: By the Angle Bisector Theorem, the angle bisectors of $\angle P$ and $\angle Q$ divide the opposite sides $QR$ and $PR$ in the ratio of the adjacent sides $PQ$ and $QR$ and $PQ$ and $PR$, respectively.

Let $A$ be the intersection of the angle bisector of $\angle P$ with $QR$, and $B$ be the intersection of the angle bisector of $\angle Q$ with $PR$. Then we have:
\[ \frac{QA}{AR} = \frac{PQ}{PR} \quad \text{and} \quad \frac{PB}{BR} = \frac{PQ}{QR} \]

By the Law of Sines, we have:
\[ \frac{PQ}{\sin \angle PRQ} = \frac{QR}{\sin \angle PQR} = \frac{PR}{\sin \angle QPR} \]

Since $\angle PRQ = 2 \angle PSQ$ and $\angle PQR = 2 \angle QSP$, we have:
\[ \frac{PQ}{\sin 2 \angle PSQ} = \frac{QR}{\sin 2 \angle QSP} \]

Using the double-angle formula, we have:
\[ \frac{PQ}{2 \sin \angle PSQ \cos \angle PSQ} = \frac{QR}{2 \sin \angle QSP \cos \angle QSP} \]

Since $\angle PSQ + \angle QSP = 90^\circ$, we have:
\[ \cos \angle PSQ = \sin \angle QSP \quad \text{and} \quad \cos \angle QSP = \sin \angle PSQ \]

Therefore, we have:
\[ \frac{PQ}{\sin \angle QSP} = \frac{QR}{\sin \angle PSQ} \]

Now, let $ST = d$. By the Law of Sines, we have:
\[ \frac{d}{\sin \angle QSP} = \frac{10}{\sin \angle PSQ} \]

By the Angle Bisector Theorem, we have:
\[ \frac{8}{10} = \frac{PQ}{QR} \]

Therefore, we have:
\[ \frac{8}{10} = \frac{\frac{d}{\sin \angle QSP}}{\frac{10}{\sin \angle PSQ}} \]

Simplifying, we get:
\[ d = \frac{8 \sin \angle QSP}{\sin \angle PSQ} \]

Using the Law of Sines again, we have:
\[ \frac{8}{\sin \angle PSQ} = \frac{10}{\sin \angle QSP} \]

Therefore, we have:
\[ d = \frac{8 \sin \angle QSP}{\sin \angle PSQ} = \frac{8 \cdot \frac{10}{8}}{\sin \angle PSQ} = \frac{10}{\sin \angle PSQ} \]

Now, by the Law of Sines, we have:
\[ \frac{10}{\sin \angle PSQ} = \frac{8}{\sin \angle QSP} \]

Therefore, we have:
\[ d = \frac{10}{\sin \angle PSQ} = \frac{8}{\sin \angle QSP} \]

Simplifying, we get:
\[ d = \boxed{10} \]