
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 plans to build an open-top rectangular tank with one fixed side length of $8m$ and a maximum water capacity of $72m^{3}$. The cost of constructing the bottom and the walls of the tank are $2a$ yuan per square meter and $a$ yuan per square meter, respectively. How should the tank be designed in terms of the length of the other side of the bottom and the height of the tank to minimize the total construction cost? What is the minimum cost?

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