
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
(The full score of this question is 14 points) Construct a rectangular covered water pool with a volume of 18 cubic meters and a depth of 2 meters. If the cost per square meter for the pool bottom and the pool walls is 200 yuan and 150 yuan respectively, how should the pool be constructed to minimize the cost, and what would be the minimum cost?

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