
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 circle of radius $3$ is divided into five congruent arcs. These arcs are rearranged to form a pentagram inside a regular pentagon, which is inscribed in the original circle. What is the ratio of the area of the pentagram to the area of the original circle?
A) $\frac{5\sqrt{25 + 10\sqrt{5}}}{32\pi}$
B) $\frac{5\sqrt{25 + 10\sqrt{5}}}{16\pi}$
C) $\frac{5\sqrt{5}}{8\pi}$
D) $\frac{5\sqrt{25 + 10\sqrt{5}}}{24\pi}$
E) $\frac{5\sqrt{5}}{32\pi}$

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