
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, and angle bisector \(\overline{PS}\) intersects \(\overline{MN}\) at \( X \). If \( PM = 2, MQ = 6, PN = 3, \) and \( NR = 9, \) compute \(\frac{PX}{PS}\).

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