
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 10 units. Congruent circular arcs with radius 4 units are drawn with centers at each vertex of the hexagon, forming sectors of 72 degrees each. Calculate the area of the region inside the hexagon but outside the sectors.
A) $150\sqrt{3}$
B) $19.2\pi$
C) $150\sqrt{3} + 19.2\pi$
D) $150\sqrt{3} - 19.2\pi$
E) $130\sqrt{3} - 16\pi$

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