
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
What is the volume of the hemisphere? Give your answer in terms of $\pi$.

In a right circular cone standing inside a right cylinder of the same base radius $r$ and height $h$, express the volume of the space between them in terms of $r$ and $h$.

Find the ratio of the volume of the cylinder to that of the cone.

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