
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 $PQR,$ points $M$ and $N$ are on $\overline{PQ}$ and $\overline{PR},$ respectively, such that $PM = 2$ and $MQ = 6$, while $PN = 3$ and $NR = 9$. The angle bisector $\overline{PS}$ of $\angle P$ intersects $\overline{MN}$ at point $L$. Compute $\frac{PL}{PS}.$

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