
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
Inside a square with a side length of $4 \mathrm{~cm}$, a circle with a diameter of $1 \mathrm{~cm}$ moves such that it always touches the perimeter of the square. Calculate the area of that part of the square which can never be covered by the moving circle.

(M. Dillingerová)

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