
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
Given rectangle $JKLM$ has $JL=8$ and $LM=6$. Point $N$ lies on $\overline{JL}$ so that $LN=2$, point $P$ lies on $\overline{LM}$ so that $PM=2$, and point $Q$ lies on $\overline{MJ}$ so that $MQ=3$. Segments $\overline{JP}$ and $\overline{JM}$ intersect $\overline{NQ}$ at $R$ and $S$, respectively. Find the value of $\frac{RS}{NQ}$.

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