
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 $XYZ$ where $\angle YXZ = 90^\circ$ and $\angle XYZ < 45^\circ$, $XY = 5$. Point $Q$ on $\overline{XY}$ is such that $\angle XQZ = 2\angle XZQ$ and $ZQ = 2$. Find $\frac{XQ}{YQ}$, which can be expressed as $m + n\sqrt{t}$, where $m$, $n$, $t$ are positive integers and $t$ is not divisible by the square of any prime. Determine $m+n+t$.

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