
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
A piece of cheese is located at $(15, 12)$ in a coordinate plane. A mouse is at $(3, -3)$ and is running up the line $y = -4x + 9$. At which point $(a, b)$ does the mouse start getting farther from the cheese rather than closer to it? What is $a + b$?

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