
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 rectangular base of dimensions $a \times b$ and height $h$ is to be wrapped with a square sheet of wrapping paper. The box is centered on the wrapping paper with the vertices of the base lying along the midlines of the square sheet of paper. The wrapping paper is folded such that the corners of the wrapping paper meet at the center of the top of the box, point $A$. Determine the area of the square sheet of wrapping paper necessary for this wrapping.
A) $(a + h)^2$
B) $(b + 2h)^2$
C) $(a + 2h)^2$
D) $2(a + h)^2$
E) $a^2 + b^2 + 4h^2$

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