
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
A cone is inscribed in a hemisphere; the vertex of the cone coincides with the center of the circle that forms the base of the hemisphere; the planes of the bases of the cone and the hemisphere are parallel. A line passing through the center of the base of the cone and an arbitrary point on the circumference of the great circle of the hemisphere forms an angle \(\alpha\) with the plane of the base of the cone. Find the ratio of the volumes of the hemisphere and the cone.


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