
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 unit plans to build an open-top rectangular water tank with a volume of $48m^3$ and a depth of $3m$. The cost of constructing the bottom of the tank is $40$ yuan per square meter, and the cost of constructing the walls is $20$ yuan per square meter. What dimensions should the tank have to minimize the total construction cost, and what is the minimum total cost?

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