
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 the circle: $x^2+y^2-4x-6y+12=0$.
1. Find the equation of the tangent line to the circle that passes through point A $(3, 5)$.
2. For any point P $(x, y)$ on the circle, find the maximum and minimum values of $\frac{y}{x}$.

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