
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 its base radius equal to \(a\), is inscribed in a right rectangular prism, where the base of the prism is a rectangle with side lengths \(2a\) and \(3a\) (twice and thrice the diameter of the cone's base respectively). The heights of both the cone and prism are \(h\). 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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