
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 and is tangent to all sides of the base. The base of the prism has length $a = 4r$ and width $b = 2r$, with $r$ being the radius of the cone's base. If the height of both the cone and the prism 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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