
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 cylinder is inscribed in a cube such that the cylinder's height equals the side length of the cube and its diameter is equal to the side length of the cube. Calculate the ratio of the volume of the inscribed cylinder to the volume of the cube, and express your answer as a common fraction in terms of $\pi$.

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