
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 rectangle and a regular pentagon have the same perimeter. Let $A$ be the area of the circle circumscribed about the rectangle, with the rectangle having side lengths in the ratio 3:1, and $B$ the area of the circle circumscribed around the pentagon. Find $A/B$.
A) $\frac{125(\sqrt{5}-1)}{256}$
B) $\frac{5}{3} \cdot \frac{5-\sqrt{5}}{8}$
C) $\frac{500(5 - \sqrt{5})}{1024}$
D) $\frac{5(5-\sqrt{5})}{64}$
E) $\frac{250(5 - \sqrt{5})}{256}$

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