
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 $M$ and $N$ are on $\overline{XY}$ and $\overline{XZ}$, respectively, and angle bisector $\overline{XP}$ intersects $\overline{MN}$ at $Q$. If $XM = 2$, $MY = 6$, $XN = 3$, and $NZ = 9$, compute $\frac{XQ}{XP}$.

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