
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 equation of circle $C$: $x^2 + y^2 - 2mx - 2y + 4m - 4 = 0$ ($m \in \mathbb{R}$).

(1) Find the value of $m$ that minimizes the area of circle $C$.

(2) Find the equation of the line that is tangent to circle $C$ under the condition found in (1) and passes through the point $(1, -2)$.

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