
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 hexagon with a side length of 4 units. Outside of each vertex of the hexagon, a quarter-circle is drawn with radius equal to the side length of the hexagon. Calculate the area of the region inside the hexagon and outside all the quarter-circles.
A) \( 48\sqrt{3} - 24\pi \)  
B) \( 24\sqrt{3} - 12\pi \)  
C) \( 72\sqrt{3} - 36\pi \)  
D) \( 36\sqrt{3} - 18\pi \)

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