
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
To solve the difficulty of drinking water for the residents in the old district of Yichang, the Yichang Municipal Government plans to help build a rectangular, lidless water tank with a volume of $4800m^{3}$ and a depth of $3m$. If the cost per square meter of the tank bottom is $150$ yuan and the cost per square meter of the tank wall is $120$ yuan, please help design the water tank to minimize the total construction cost. What is the lowest total construction cost?

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