
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
Point $G$ is taken on side $AB$ of square $WXYZ$. At $Z$, a perpendicular is drawn to $ZG$, meeting $WY$ extended at $H$. The area of square $WXYZ$ is $324$ square inches, and the area of $\triangle ZGH$ is $234$ square inches. Find the number of inches in $WH$.
A) $6\sqrt{26}$  
B) $12\sqrt{11}$  
C) $18\sqrt{11}$  
D) $28$  
E) $36$

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