
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 sheet of paper has dimensions such that its length is 2 times its width and has an area \( A \). The paper is divided into four equal sections along its length. A dotted line is then drawn from the first quarter point to the third quarter point on the opposite side. The paper is folded along this dotted line, forming a new area \( B \). Calculate the ratio \( \frac{B}{A} \).
**A)** $\frac{1}{2}\qquad$ **B)** $\frac{7}{8}\qquad$ **C)** $1 - \frac{\sqrt{2}}{8}\qquad$ **D)** $\frac{3}{4}\qquad$ **E)** $\frac{4}{5}$

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