
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
A square with side length 4 contains four quarter-circles within it, each having a radius equal to half the side length of the square. The quarter-circles are positioned so that their curved edges touch each other, and each quarter-circle's straight edges lie along two sides of the square. Determine the area of the region inside the square but outside all the quarter-circles.

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