
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 $10\times15$ rectangle $ABCD$ is cut into two congruent hexagons, which are then repositioned without overlap to form a square. Find the dimension $y$, assuming it is half the length of a side of the square.
A) $\frac{5\sqrt{2}}{2}$  
B) $\frac{5\sqrt{3}}{2}$  
C) $\frac{5\sqrt{4}}{2}$  
D) $\frac{5\sqrt{5}}{2}$  
E) $\frac{5\sqrt{6}}{2}$

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