
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 box with a rectangular base is to be wrapped with a square sheet of wrapping paper. The box, which has a length of $2w$ and a width of $w$ (creating a 2:1 rectangle), and height $h$, is centered on the wrapping paper with its longer sides parallel to the edges of the paper. The vertices of the base lie on the midlines of the wrapping paper. The wrapping paper is folded up the sides and brought together to meet at the center of the top of the box, point $A$. Calculate the area of this sheet of wrapping paper.

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