
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 inside a cube. Its height is equal to the cube's side length, and the diameter of the cylinder's base is also equal to the cube's side length. 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}
user