
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 $ABCD$ has $AB=8$ and $BC=6$. Point $H$ lies on $\overline{AB}$ so that $BH=3$, point $I$ lies on $\overline{BC}$ so that $CI=2$, and point $J$ lies on $\overline{CD}$ so that $DJ=3$. Segments $\overline{AI}$ and $\overline{AC}$ intersect $\overline{HJ}$ at $R$ and $S$, respectively. Find the value of $\frac{RS}{HJ}$.

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