
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]


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The circumference of radius \(R\) is divided into six equal arcs, and within the circle formed by this circumference, equal arcs of such radius are drawn through every two neighboring division points so that they mutually touch on the given circumference. Calculate the area of the inner part of the given circle enclosed by the drawn arcs.

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