
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 sports stadium plans to build a rectangular swimming pool with a volume of 4800m<sup>3</sup> and a depth of 3m. If the unit price for constructing the pool walls is $a$ and the unit price for constructing the pool bottom is 1.5 times that of the walls, how should the length and width of the pool be designed to minimize the total construction cost? What is the minimum cost?

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