
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 $\triangle XYZ$, where $XY=9$, $YZ=12$, and $ZX=15$, and $\overline{XJ}$ is an altitude. Points $K$ and $L$ are on sides $\overline{ZX}$ and $\overline{XY}$, respectively, with $\overline{YK}$ and $\overline{ZL}$ being angle bisectors meeting $\overline{XJ}$ at $R$ and $S$, respectively. Determine the length of $RS$.

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