
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 with radius \( r \) and a segment \( AB \) parallel to the plane of the circle at a distance \( r \) from the plane. The perpendicular projection of segment \( AB \) onto the plane of the circle is a diameter of the circle. From each interior point of the segment \( AB \), draw two rays perpendicular to \( AB \) that intersect the circle, and from the endpoints, draw one ray. Determine the volume of the solid bounded by the circular plane and these rays.

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