
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 an equilateral triangle have the same perimeter. The length of the rectangle is twice its width. Let $C$ be the area of the circle circumscribed around the rectangle and $D$ the area of the circle circumscribed around the triangle. Find the ratio $\frac{C}{D}$.
A) $\frac{1}{2}$
B) $\frac{2}{3}$
C) $\frac{15}{16}$
D) $\frac{5}{6}$
E) $\frac{12}{13}$

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