
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 has a volume of $72\pi$ $\text{cm}^3$. Calculate the combined volume of a cone with the same height as the cylinder and a hemisphere that fits exactly on the top of the cylinder's open end. The radius of the hemisphere is equal to the radius of the cylinder and the cone. Express your answer in terms of $\pi$.

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