
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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A square and an equilateral triangle are circumscribed around a circle of radius \( R \), with one of the sides of the square lying on the side of the triangle. Calculate the area of the common part of the triangle and the square.

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