
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 sphere O with a radius of 2, a cone is inscribed in the sphere O. When the volume of the cone is maximized, find the radius of the sphere inscribed in the cone.

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