
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 cut into six congruent arcs. These arcs are then rearranged symmetrically to form a hexagonal star as illustrated below. Determine the ratio of the area of the hexagonal star to the area of the original circle.
A) $\frac{4.5}{\pi}$
B) $\frac{4.5\sqrt{2}}{\pi}$
C) $\frac{4.5\sqrt{3}}{\pi}$
D) $\frac{9\sqrt{3}}{\pi}$
E) $\frac{6\sqrt{3}}{\pi}$

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