
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 a length that is twice the width, and the area of the paper is $A$. This 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 along this dotted line to create a new shape with area $B$. What is the ratio $\frac{B}{A}$?
A) $\frac{1}{2}$
B) $\frac{2}{3}$
C) $\frac{3}{4}$
D) $\frac{1}{3}$
E) $\frac{4}{5}$

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