
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 right circular cylinder is inscribed in a right circular cone. The cone has diameter 12 and altitude 18, and the axes of the cylinder and cone coincide. The diameter of the cylinder is equal to its height. Find the radius of the cylinder. Express your answer as a common fraction.

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