
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
An open box is constructed by starting with a rectangular sheet of metal \(12\) in. by \(16\) in. and cutting a square of side \(x\) inches from each corner. The resulting projections are folded up and the seams welded. The volume of the resulting box is:
**A)** \( 4x^3 - 56x^2 + 192x \)  
**B)** \( 192x - 56x^2 + 4x^3 \)  
**C)** \( 192x + 28x^2 + x^3 \)  
**D)** \( 192x - 28x^2 + x^3 \)  
**E)** \( \text{none of these} \)

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