
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 wants to build a rectangular water tank without a lid, with a volume of $4800m^{3}$, and a depth of $3m$. If the cost of constructing the pool's bottom is $150$ yuan per $m^{2}$, and the cost of constructing the pool's walls is $120$ yuan per $m^{2}$, how should the water tank be designed to minimize the total construction cost? What is this minimum total cost?

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