
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 unit square and 5 equal disks. Four of the disks are positioned such that they touch two adjacent sides of the square from the inside (without overlapping). The fifth disk is moved within the part of the square that is not covered by the stationary disks. What is the area that the moving disk can sweep over during its movement?

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