
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 rectangular piece of paper has dimensions such that its length is twice its width. If the width of the paper is $w$, the paper is divided into four equal sections along the length. A dotted line is then drawn from the first divider to the third divider on the opposite side. The paper is then folded entirely along this line, and the resulting shape overlaps partially. Calculate the area of the overlapped region after folding.
A) $\frac{w^2}{4}$
B) $\frac{w^2}{2}$
C) $\frac{3w^2}{4}$
D) $w^2$
E) $\frac{5w^2}{4}$

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