
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
Ann inscribed a circle inside a regular hexagon, circumscribed a circle around the hexagon, and calculated the area of the region between the two circles. Bob did the same with a regular octagon (8 sides). The areas of the two regions were $C$ and $D$, respectively. Each polygon had a side length of $3$. Which of the following is true?
A) $C = \frac{7}{5} D$
B) $C = D$
C) $C = \frac{9}{4} D$
D) $C = \frac{4}{5} D$
E) $C = \frac{5}{4} D$

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