
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
A square and a regular pentagon have the same perimeter. Let $C$ be the area of the circle circumscribed about the square, and $D$ the area of the circle circumscribed around the pentagon. Find $C/D$.
A) $\frac{25}{128}$
B) $\frac{25(5 + 2\sqrt{5})}{128}$
C) $\frac{25(5-2\sqrt{5})}{128}$
D) $\frac{5\sqrt{5}}{128}$

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