
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
Given a triangle \( ABC \) in the Cartesian plane with an area of \( 56 \). The coordinates of \( B \) and \( C \) are \( (10, 15) \) and \( (20, 16) \), respectively. The coordinates of \( A \) are \( (p, q) \). The line containing the median to side \( BC \) has a slope of \( -3 \). Find the maximum possible value of \( p + q \).

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