
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 circle C: x² + y² - 8y + 12 = 0, and line l passes through point P(-2, 0).
(1) Find the equation of line l if it is tangent to circle C.
(2) Find the equation of line l if it intersects circle C at points A and B, and $| \overrightarrow {AB}|=2 \sqrt {2}$.

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