
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 prism such that the base of the cylinder touches all four sides of the square base of the prism. The height of the cylinder is the same as the height of the prism. What is the ratio of the volume of the cylinder 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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