
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 $XYZ$ lies in the cartesian plane and has an area of $56$. The coordinates of $Y$ and $Z$ are $(15,24)$ and $(27,25),$ respectively, and the coordinates of $X$ are $(p,q).$ The line containing the median to side $YZ$ has slope $-3.$ Find the largest possible value of $p+q.$

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