
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 container without a lid, with a volume of $8 \text{m}^3$, a height of no less than $3 \text{m}$, and a length of $2 \text{m}$ for the bottom rectangle. Given that the cost of constructing the bottom surface is $40\text{￥}$ per square meter and the cost of constructing the lateral surfaces is $20\text{￥}$ per square meter, find the minimum total cost of the container and the width of the bottom rectangle at this cost.

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