
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 $G$ and $H$ are on $\overline{PQ}$ and $\overline{PR},$ respectively, and angle bisector $\overline{PS}$ intersects $\overline{GH}$ at $J.$ If $PG = 2,$ $GQ = 6,$ $PH = 3,$ and $HR = 5,$ compute $\frac{PJ}{PS}.$

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