
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 cube. The height of the cylinder equals the side length of the cube, and the diameter of the cylinder's base equals the side length of the cube. What is the ratio of the volume of the inscribed cylinder to the volume of the cube?

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