
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 $10\times15$ rectangle $EFGH$ is cut into two congruent pentagons, which are repositioned to form a square. Determine the length $z$ of one side of the pentagons that aligns with one side of the square.
A) $5\sqrt{2}$   
B) $5\sqrt{3}$  
C) $10\sqrt{2}$   
D) $10\sqrt{3}$

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