
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 cone with height \(h\) and radius \(r\) is inscribed in a right prism, which has a square base with side length \(2r\) and height \(2h\). Calculate 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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