
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 circle and a chord within it, where the length of the chord is equal to the side of an equilateral triangle inscribed in the circle. The chord is rotated around the center of the circle by $90^{\circ}$. What area does the chord sweep out during this rotation?

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