
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 9x16 rectangle ABCD is cut into two congruent quadrilaterals, as shown, in such a way that the two quadrilaterals can be repositioned without overlap to form a square. What is the value of \( z \), which represents the length of a side of one quadrilateral?
A) 10  
B) 11  
C) 12  
D) 13  
E) 14

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