
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 and an inscribed square have one side each that is parallel to the other. Calculate the area of the part of the circle that lies between the parallel sides of the hexagon and the square and does not contain the center of the circle.

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