
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 \( C: (x-1)^{2} + (y-2)^{2} = 2 \) and the point \( P(2, -1) \), draw the tangents to the circle \( C \) passing through \( P \). Let \( A \) and \( B \) be the points of tangency. Find the equation of the line \( AB \).

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