
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 of one unit has quarter-circle arcs with a radius of one unit drawn around each vertex, connecting it to the adjacent vertices. Calculate the area of the common region shared by the four circular segments.

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