
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 side length \(a\), a semicircle is constructed on each side, using the side as the diameter. Find the area of the rosette enclosed by the arcs of the semicircles.

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