
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 vertex \( A \) of a regular prism \( ABC A_{1}B_{1}C_{1} \) coincides with the apex of a cone, vertices \( B \) and \( C \) lie on the lateral surface of this cone, and vertices \( B_{1} \) and \( C_{1} \) lie on the circumference of its base. Find the ratio of the volumes of the cone and the prism, if \( \left|A A_{1}\right| = 2.4 |A B| \).

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