
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
Design a rectangular pool without a cover that has a volume of 4800 m³ and a depth of 3 m. Given the construction cost per square meter is 150 yuan for the pool bottom and 120 yuan for the pool walls, 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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