
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 a side length of 4, six semicircles are inscribed such that their diameters coincide with the sides of the hexagon. Additionally, segments are drawn connecting the centers of opposite semicircles. Calculate the area of the region inside the hexagon but outside all of the semicircles and segments.
A) $24\sqrt{3} - 6\pi$
B) $36\sqrt{3} - 9\pi$
C) $48\sqrt{3} - 12\pi$
D) $60\sqrt{3} - 15\pi$
E) $72\sqrt{3} - 18\pi$

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