
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
Construct a rectangular open-top pool with a volume of $18 \text{ m}^3$ and a depth of $2 \text{ m}$. If the cost per square meter for the bottom and the walls is 200 yuan and 150 yuan respectively, calculate the minimum total cost for constructing the pool.

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