
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
Given a rectangular piece of sheet metal with a length of 90 cm and a width of 48 cm, create an open-top container by cutting out a small square at each of the four corners. The sides are then bent at right angles to form the container. What should be the height of the container to maximize its volume, and what is the maximum volume?

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