
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
Four unit circles are placed on a square of side length  $2$ , with each circle centered on one of the four corners of the square. Compute the area of the square which is not contained within any of the four circles.

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