
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 pyramid is placed inside a cone; the base of the pyramid is inscribed in the base of the cone, and the apex of the pyramid lies on one of the generating lines of the cone. All lateral faces of the pyramid are equally inclined to the base plane. The base of the pyramid is an isosceles triangle with an angle \(\alpha(\alpha \geq \frac{\pi}{3})\) at the vertex. Find the ratio of the volumes of the cone and the pyramid.

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