You will receive a question-answer pair and be asked to provide a response in JSON format. For each answer:

1. *For accepted answers*: Write the answer as a series of numbered steps (e.g., "Step 1", "Step 2", etc.). After each step, include a confidence score in parentheses, ranging from 0 to 1, where the score progressively increases toward the final answer.
   
2. *For rejected answers*: Include incorrect reasoning steps. Keep confidence scores inconsistent or lower to indicate flawed logic.

### JSON Output Structure

{
  "prompt": "[Question text]",
  "chosen": [
    {
      "content": "[Insert question text]",
      "role": "user"
    },
    {
      "content": "[Accepted answer as step-by-step reasoning, with confidence scores in parentheses after each step.]",
      "role": "assistant"
    }
  ],
  "rejected": [
    {
      "content": "[Insert question text]",
      "role": "user"
    },
    {
      "content": "[Rejected answer with flawed steps, each followed by a confidence score in parentheses.]",
      "role": "assistant"
    }
  ]
}

---

### Example Output

{
  "prompt": "How can I develop a habit of drawing daily?",
  "chosen": [
    {
      "content": "How can I develop a habit of drawing daily?",
      "role": "user"
    },
    {
      "content": "To build a daily drawing habit, try these steps:\n\nStep 1: Set aside a specific time each day for drawing to build consistency (confidence: 0.7).\nStep 2: Start with a short time commitment, like 5–10 minutes, to make it manageable (confidence: 0.8).\nStep 3: Track your progress to stay motivated as you see improvement over time (confidence: 0.9).\nStep 4: Gradually extend your drawing time as it becomes a natural part of your routine (confidence: 1.0).\n\nFollowing these steps can help establish a sustainable and rewarding daily drawing habit.",
      "role": "assistant"
    }
  ],
  "rejected": [
    {
      "content": "How can I develop a habit of drawing daily?",
      "role": "user"
    },
    {
      "content": "To build a drawing habit:\n\nStep 1: Draw only when feeling inspired, which may not be consistent (confidence: 0.4).\nStep 2: Set high standards for each drawing session, aiming for completed artwork (confidence: 0.3).\nStep 3: Take breaks for a few days if you feel tired, to avoid burnout (confidence: 0.2).\n\nThis approach may not support a daily habit, as it relies on sporadic inspiration rather than consistency.",
      "role": "assistant"
    }
  ]
}


Question: Find the interval of all $y$ such that both $4y$ and $5y$ are in the interval $(2,3)$.
Answer: Given that $4y$ and $5y$ are both in the interval $(2,3)$, we can set up the following inequalities:

1. For $4y$:
\[ 2 < 4y < 3 \Rightarrow \frac{1}{2} < y < \frac{3}{4} \]

2. For $5y$:
\[ 2 < 5y < 3 \Rightarrow \frac{2}{5} < y < \frac{3}{5} \]

To find the interval where both conditions are true, we find the overlap between these two intervals.

The intersection of the intervals $\left(\frac{1}{2}, \frac{3}{4}\right)$ and $\left(\frac{2}{5}, \frac{3}{5}\right)$ is $\left(\frac{1}{2}, \frac{3}{5}\right)$.

Therefore, the interval of all $y$ such that both $4y$ and $5y$ are in the interval $(2,3)$ is:
\[ \boxed{\left(\frac{1}{2}, \frac{3}{5}\right)} \]