
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
A rectangular metal sheet is 12 in. by 16 in. From each corner, squares with side length $x$ inches are removed to create an open box by folding up the flaps. Given that the cuts must allow a feasible box, and the sides of the box must be positive, find the maximum volume of the box that can be created.

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