
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 $PM = 2,$ $MQ = 6,$ $PN = 3,$ and $NR = 9.$ The angle bisector $\overline{PS}$ intersects $\overline{MN}$ at $T.$ Compute $\frac{PT}{PS}.$

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