
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 dimensions $l$ for length, $w$ for width, and $h$ for height needs to be wrapped with a square sheet of wrapping paper. The box is placed such that its longest side ($l$) lies along the midline of the wrapping paper, extending equal distances from the center to the left and right edges of the wrapping paper. The other dimension of the box ($w$) is centered along the perpendicular midline of the wrapping paper. All eight corners of this paper are brought up and secured at the center of the top of the box, at point $A$. What is the area of the wrapping paper needed?
A) $4 \left(\frac{l}{2} + h\right)^2$
B) $4 \left(\frac{w}{2} + h\right)^2$
C) $\left(\frac{l}{2} + h\right)^2 + \left(\frac{w}{2} + h\right)^2$
D) $\max\left(\frac{l}{2} + h, \frac{w}{2} + h\right)^2$
E) $4 \max\left(\frac{l}{2} + h, \frac{w}{2} + h\right)^2$

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