
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 needs to build an open-topped rectangular prism water storage tank with a volume of 4800 cubic meters and a depth of 3 meters. The construction cost per square meter for the bottom of the tank is 150 yuan, and the cost per square meter for the walls is 120 yuan. Assume the length of the rectangular bottom is x meters.
(1) Express the surface area S of the walls using an expression that includes x.
(2) How should the tank be designed to minimize the total construction cost? What is the minimum cost?

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