
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 sheet of metal measures $12$ in. by $16$ in. Squares with side length $x$ inches are cut from each corner, and the sides are then folded to form an open box. Additionally, to ensure the structural integrity of the box, the side length $x$ must not exceed the width of the material divided by $5$. Determine the expression for the volume of the box.

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