
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
From a point $P(-2, 3)$ outside the circle $C: (x-1)^2 + (y-1)^2 = 1$, tangents are drawn to the circle $C$, touching the circle at points $M$ and $N$.
(1) Find the equations of the tangents;
(2) Find the equation of the line passing through the two points of tangency.

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