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

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