
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
In trapezoid $WXYZ$ where $\overline{WZ} \parallel \overline{XY}$, $\overline{WX} = \overline{YZ} = 24$, $\overline{WY}$ is perpendicular to $\overline{XY}$. The diagonals $\overline{WY}$ and $\overline{XZ}$ intersect at point $O$, and point $Q$ is the midpoint of $\overline{XY}$. It is given that $OQ = 9$. The length of $WY$ can be expressed in the form $a\sqrt{b}$, where $a$ and $b$ are positive integers and $b$ is not divisible by the square of any prime. What is $a+b$?
A) 65  
B) 71  
C) 78  
D) 85  
E) 92

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