
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
The radius of the base of a right circular cylinder is 6, and its height is 8. On the circumference of the top base, points \( X \) and \( Y \) are marked such that one of the arcs between points \( X \) and \( Y \) measures \( 120^{\circ} \). Find the area of the cross-section of the cylinder by a plane passing through points \( X \), \( Y \), and the center of the cylinder. If necessary, round the answer to two decimal places.

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