
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
Calculate the volume of the largest right circular cylinder that can be inscribed in a given right circular cone. What percentage is the volume of this cylinder compared to the volume of the cone? (The base of the inscribed cylinder is in the base of the cone, and the other circle of the cylinder is a plane section of the cone.)

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