
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 a square \(ABCD\) with side length 1 centimeter, draw quarter circles centered at \(A\), \(B\), \(C\), and \(D\) with a radius of 1 centimeter. The intersection points are \(E\), \(F\), \(G\), and \(H\). What is the perimeter of the shaded area in the middle? ___ centimeters.

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