
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 $PQR$ lies in the cartesian plane and has an area of $85$. The coordinates of $Q$ and $R$ are $(14, 20)$ and $(27, 22)$, respectively, and the coordinates of $P$ are $(x, y)$. The line containing the median to side $QR$ has slope $-2$. Find the largest possible value of $x+y$.

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