
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 is building a rectangular prism-shaped open water reservoir with a volume of $4800$ cubic meters and a depth of $3$ meters. The cost of constructing the pool's bottom is $150$ yuan per square meter, while the cost of constructing the pool's walls is $120$ yuan per square meter. Let $x$ be the length of the rectangular bottom of the pool.

(I) Find the area of the bottom and express the area of the walls using an expression containing $x$.

(II) How should the pool be designed to minimize the total cost? What is the minimum total cost?

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