
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 square pedestal of height \( p \) supports a closed box with a square base, which in turn is to be wrapped with a square sheet of wrapping paper. The box and pedestal together are centered on the wrapping paper, with the vertices of the box's base on the paper's midlines. The four corners of the wrapping paper are folded up over the sides of the pedestal and the box, meeting at point \( A \) atop the box. The box has a base length \( w \) and height \( h \). Determine the area of the sheet of wrapping paper.
**A)** \( 2w(p+h) \)  
**B)** \( 4w(p+h) \)  
**C)** \( 4w^2 \)  
**D)** \( 4w^2 + 4wh \)  
**E)** \( (w+p+h)^2 \)

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