
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
Two circles of radius $R$ intersect in such a way that each circle passes through the center of the other. Two additional circles of the same radius have their centers at the intersection points of the first two circles. Find the area common to all four circles.

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