
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
If the perimeter of a rectangle is \( p \) and its diagonal is \( d \), and one side is twice the length of the other side, the difference between the length and width of the rectangle is:
- **A)** \( \frac{p}{4} \)
- **B)** \( \frac{p}{6} \)
- **C)** \( \frac{p}{8} \)
- **D)** \( \frac{p}{12} \)
- **E)** \( \frac{p}{5} \)

Present the answer in LaTex format: \boxed{Your answer}
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