
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 as shown. The base of the prism has dimensions, where one side is exactly twice the length of the other ($a$ and $2a$). The cone's base fits perfectly into the base of the prism making one side of the rectangle the diameter of the cone's base. The height of the prism and the height of the cone are equal. Calculate the ratio of the volume of the cone to the volume of the prism, and express your answer as a common fraction in terms of $\pi$.

Present the answer in LaTex format: \boxed{Your answer}
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