
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
Triangle $XYZ$ has a right angle at $Z$ with $\angle YXZ < 45^\circ$ and $XY = 5$. Point $P$ is on $\overline{XY}$ such that $\angle XPZ = 2\angle XPY$ and $ZP = 2$. Determine the ratio $\frac{XP}{YP}$ and express it as $p + q\sqrt{r}$ where $p$, $q$, $r$ are integers.

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