
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 $XZ$ is the hypotenuse, $\angle YXZ = 30^\circ$ and $XZ = 8$. A point $Q$ on line $XZ$ satisfies $XQ = 3YZ$. Point $R$ on segment $XZ$ is such that $\angle YZR = 3\angle YRZ$. Find the ratio $\frac{XR}{RZ}$ in the simplest form.

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