
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 $\triangle XYZ$, $XY = 14$, $\angle X = 45^\circ$, and $\angle Z = 15^\circ$. Let $G, E$, and $L$ be points on the line $YZ$ such that $XG \perp YZ$, $\angle XYE = \angle EYX$, and $YL = LZ$. Point $Q$ is the midpoint of segment $GL$, and point $S$ is on ray $XE$ such that $SQ \perp YZ$. Compute $XS^2$.

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