
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
In a circle of radius \( R \), two parallel chords are drawn on opposite sides of the center. One of the chords is equal to the side of an inscribed equilateral triangle, and the other is equal to the side of an inscribed regular hexagon. Determine the area of the part of the circle that lies between the chords.

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