
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 starts at $(3,-3)$ and follows the path described by the line $y = -3x + 12$. Determine the point $(a, b)$ where, as the mouse approaches this point, it starts to move away from the cheese. Calculate $a + b$.

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