
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 is inscribed in a right rectangular prism. The base of the cone is tangent to all four sides of the rectangular base of the prism. If the base of the rectangle has side lengths $a$ and $b$, and the height of both the prism and the cone is $h$, 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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