
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 manufacture a rectangular container without a lid, with a volume of $4m^3$ and a height of $1m$, it is known that the cost of the base per square meter is $20$ yuan, and the cost of the side per square meter is $10$ yuan. What should be the dimensions of the base of the container to minimize the total cost of the container, and what is the minimum cost?

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