
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
Suppose you have a square piece of paper, 6 inches on each side. You fold the paper in half vertically. After folding, you make a cut halfway through the height, but only on the top layer, creating a flap. Then, you make another cut on the folded side, cutting all layers completely, parallel to the first fold, but only up to the horizontal cut. Determine the ratio of the perimeter of the flap to the perimeter of the largest rectangle formed.
A) $\dfrac{1}{2}$ 
B) $\dfrac{2}{3}$
C) $\dfrac{3}{4}$
D) $\dfrac{4}{5}$
E) $\dfrac{5}{6}$

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