
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 C: $x^2+y^2-4x-6y+12=0$, and the point A(3, 5).
(1) Find the equation of the tangent line to the circle passing through point A;
(2) Let point O be the origin of coordinates, connect OA and OC, calculate the area $S$ of $\triangle AOC$.

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