
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 factory produces a cylindrical open-top ice cream cone wrapper with a volume of $27\pi \text{ cm}^3$. A client orders this cylindrical wrapper and specifies that when the material used to produce the wrapper is at its minimum, the base radius $r$ of the cylinder should be ____ cm.

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