
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 $DEF$ is situated in the Cartesian plane, with an area of $50$. The coordinates of $D$ and $E$ are $(10, 15)$ and $(20, 18)$, respectively, and the coordinates of $F$ are $(r, s)$. The line containing the median to side $DE$ has a slope of $-3$. Compute the greatest possible value of $r + s$.

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