
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 an open-top rectangular pool with a volume of $18m^3$ and a depth of $2m$. If the cost per square meter for the bottom and the walls of the pool is $200$ yuan and $150$ yuan respectively, then the minimum cost of constructing this pool is (Unit: yuan).

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