
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 8 units. Each vertex of the hexagon serves as the center for drawing a congruent circular arc with a radius of 5 units that subtend an angle of 90 degrees at each vertex, covering parts of neighboring vertices. Calculate the area of the region inside the hexagon but outside the larger circular sectors.
A) $96\sqrt{3} - 25\pi$
B) $96\sqrt{3} - 37.5\pi$
C) $96\sqrt{3} - 56\pi$
D) $96\sqrt{3} - 50\pi$
E) $192\sqrt{3} - 37.5\pi$

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