
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
In a regular hexagon with side length 3, six semicircles with diameters equal to the sides of the hexagon are inscribed. Additionally, a circle with radius 1 is inscribed centrally within the same hexagon. Calculate the area of the region inside the hexagon but outside all the semicircles and the central circle.
A) $13.5\sqrt{3} - 6.75\pi$
B) $13.5\sqrt{3} - 7.75\pi$
C) $14.5\sqrt{3} - 7.75\pi$
D) $13.5\sqrt{3} - 8.75\pi$

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