
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 type of lidless ice cream paper cone in the shape of a cylinder. A customer has ordered this cylindrical paper cone and requires its volume to be $27\pi \text{cm}^{3}$. If the base radius of the cylindrical paper cone is denoted as $r$, then to minimize the material used for making this cylindrical paper cone, the value of $r$ should be _______ $\text{cm}$.

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