
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 $XYZ$ with a right angle at $Z$, $\angle ZXY < 45^\circ$ and $XY = 5$. A point $Q$ on $\overline{XY}$ is such that $\angle QZY = 2\angle ZQY$ and $ZQ = 2$. Find the ratio $\frac{XQ}{YQ}$, which can be expressed as $s + t\sqrt{u}$, where $s$, $t$, $u$ are positive integers and $u$ is not divisible by the square of any prime. Determine $s+t+u$.

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