
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 open-top water tank with a volume of $6400m^{3}$ and a depth of $4m$. If the cost of constructing the pool's bottom is $300$ yuan per $m^{2}$, and the cost of constructing the pool's walls is $240$ yuan per $m^{2}$, how should the water tank be designed to minimize the total construction cost? What is the minimum total construction cost?

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