
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 the angle bisector $\overline{XS}$ intersects $\overline{PQ}$ at $R$. If $XP = 2$, $PY = 6$, $XQ = 3$, and $QZ = 9$, compute $\frac{XR}{XS}$.

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