
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 \( DEF \) lies in the Cartesian plane and has an area of \( 50 \). The coordinates of \( D \) and \( E \) are \( (10, 15) \) and \( (20, 16) \), respectively, and the coordinates of \( F \) are \( (u, v) \). The line containing the median to side \( DE \) has slope \( -3 \). Find the largest possible value of \( u+v \).

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