
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
A regular hexagon has a side length of 3. Inside it, three semicircles are inscribed with diameters along three sides of the hexagon consecutively. The remaining three sides each have a quarter circle of radius 1.5 inside the hexagon. Calculate the area of the shaded region which is inside the hexagon but outside all these circles.
**A)** \(13.5\sqrt{3} - 6\pi\)  
**B)** \(13.5\sqrt{3} - 3\pi\)  
**C)** \(13.5\sqrt{3} - 5.0625\pi\)  
**D)** \(13.5\sqrt{3} - 4.5\pi\)

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