
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 $10 \times 15$ rectangle is divided into two congruent polygons, which are then reassembled to form a larger rectangle with its length twice its width. What is $z$, the length of one side of the smaller rectangle formed by one of the polygons?
A) $5$
B) $5\sqrt{2}$
C) $5\sqrt{3}$
D) $10$
E) $7\sqrt{3}$

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