
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. Congruent arcs with a radius of 5 are drawn with the center at each of the vertices, creating circular sectors. The region inside the hexagon but outside these sectors is shaded. Calculate the area of the shaded region.

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