
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 a circle C: $x^2+(y-4)^2=4$, and a line $l$ passing through the point $(-2, 0)$.
(1) When line $l$ is tangent to circle C, find the general equation of line $l$;
(2) When line $l$ intersects circle C at points A and B, and $|AB| \geq 2\sqrt{2}$, find the range of values for the slope of line $l$.

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