
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  $ABC$  lies in the Cartesian Plane and has an area of 70. The coordinates of  $B$  and  $C$  are  $(12,19)$  and  $(23,20)$ , respectively, and the coordinates of  $A$  are  $(p,q)$ . The line containing the median to side  $BC$  has slope  $-5$ . Find the largest possible value of  $p+q$ .

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