
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-topped rectangular container with a volume of $4m^3$ and a height of $1m$. Given that the cost of building the base is $200$ yuan per square meter and the cost of building the sides is $100$ yuan per square meter, determine the minimum total cost to construct this container.

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