
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 closed rectangular box with a base of length $l$ and width $w$ and height $h$ needs to be wrapped with a single piece of square wrapping paper. The wrapping paper must extend 2 inches beyond the box on all sides when the box is centered on the paper. The paper is folded upward along all sides of the box and meets at point $A$, the geometric center on top of the box. Calculate the required area of the square sheet of the wrapping paper.
A) $l^2 + 4l + 4 + 2lh + 2h + h^2$
B) $l^2 + 8l + 16 + 4lh + 16h + 4h^2$
C) $l^2 + 8l + 16 + 4lh + 4h$
D) $(l+2)^2 + (w+2)^2$

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