
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
Inscribe a right circular cone within a right rectangular prism with dimensions 3 times the cone’s base radius in length and width, and equal to the cone’s height. What is the ratio of the volume of the cone to the volume of the prism? Express your answer as a common fraction in terms of $\pi$.

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