
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
Inside a regular hexagon with side length 4, six semicircles and six smaller circles (one at each vertex) lie within its perimeter. The diameters of the semicircles coincide with the sides of the hexagon, and the diameter of each smaller circle is 1. What is the area of the shaded region, i.e., inside the hexagon but outside all of the semicircles and the smaller circles?
A) $24\sqrt{3} - 12\pi$
B) $24\sqrt{3} - 15\pi$
C) $24\sqrt{3} - \frac{27\pi}{2}$
D) $48\sqrt{3} - 27\pi$
E) $12\sqrt{3} - \frac{27\pi}{2}$

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