
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
From a point on the circumference of a circle with radius \( R \), two equal chords are drawn, forming an inscribed angle of \( \alpha \) radians. Find the area of the part of the circle enclosed within this inscribed angle.

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