
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 the cartesian plane, triangle $DEF$ has an area of $65$. The coordinates of $D$ and $F$ are $(10,15)$ and $(19,18),$ respectively, and the coordinates of $E$ are $(r,s).$ The line containing the median to side $DF$ has slope $-3$. Find the largest possible value of $r+s$.

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