
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
(14 points) Use a rectangular sheet of iron that is 90cm long and 48cm wide to make a lidless container. First, cut a small square from each of the four corners, then fold the four sides at a 90-degree angle and weld them together. What should be the height of the container to maximize its volume? What is the maximum volume?

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