
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
Consider a regular octagon with side length 3, inside of which eight semicircles lie such that their diameters coincide with the sides of the octagon. Determine the area of the shaded region, which is the area inside the octagon but outside all of the semicircles.
A) $54 + 18\sqrt{2} - 9\pi$
B) $54 + 36\sqrt{2} - 9\pi$
C) $18 + 36\sqrt{2} - 9\pi$
D) $27 + 36\sqrt{2} - 4.5\pi$

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