
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 gas station needs to manufacture a cylindrical oil tank with a volume of $20 \pi \ \mathrm{m}^{3}$. The price of the iron plate used to make the bottom is 40 yuan per square meter, and the price of the iron plate used for the side is 32 yuan per square meter. Assuming no material is wasted, what should the radius and height of the bottom of the oil tank be to minimize the material cost?

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