
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 $XYZ,$ points $P$ and $Q$ are on $\overline{XY}$ and $\overline{XZ},$ respectively, and angle bisector $\overline{XU}$ intersects $\overline{PQ}$ at $R.$ If $XP = 2,$ $PY = 6,$ $XQ = 3,$ and $QZ = 3,$ compute $\frac{XR}{XU}.$

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