
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
Given a shape made of arcs of three circles, each with radius \( R \), where the centers of the circles lie on the same straight line and the middle circle passes through the centers of the other two circles, calculate the perimeter of the shape.

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