
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 $10 \times 20$ rectangle is cut into two congruent hexagons that can be rearranged to form a square. Determine the length $y$ if it is a fourth of the square's side.
A) $\frac{5\sqrt{2}}{2}$  
B) $5$  
C) $\frac{10\sqrt{2}}{2}$  
D) $\frac{5}{2}$  
E) $\sqrt{2}$

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