
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
The $10\times20$ rectangle $ABCD$ is cut into two congruent pentagons, which are then repositioned without overlap to form a square. What is $y$, if $y$ is a dimension in the pentagon such that three times $y$ equals the width of the rectangle?
A) $\frac{15}{2}$
B) $\frac{20}{3}$
C) $\frac{18}{3}$
D) $\sqrt{20}$
E) $\frac{30}{3}$

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