
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
In the diagram, each of the four identical circles touch the other two adjacent circles directly. The circumference of each circle is 72. What is the perimeter of the shaded region formed at the center where all four circles meet? Assume each pair of adjacent circles' centers form an angle of 90 degrees at the center of the shaded region.

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