
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
Three overlapping circles of radius 6 units each have centers on the vertices of an equilateral triangle. Each circle forms an arc with a central angle measure of 120 degrees that intersects the next circle at points of tangency. Compute the area of the region common to all three arcs.

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