
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
Five equal spheres are placed inside a cone. Four of them lie on the base of the cone, where each of these four spheres touches two other spheres lying on the base and the lateral surface of the cone. The fifth sphere touches the lateral surface and the other four spheres. Find the volume of the cone if the radius of each sphere is \( r \).

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