
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
Triangle $XYZ$ is positioned in the Cartesian plane with an area of $50$. The coordinates of $X$ and $Y$ are $(10,15)$ and $(20,17)$, respectively, and the coordinates of $Z$ are $(r,s)$. The line containing the median to side $XY$ has a slope of $-3$. Determine the highest possible value of $r+s$.

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