
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 - 4x + y² + 3 = 0.
(1) Find the value of m for the line l that passes through point P(0, 1) with slope m and is tangent to circle C.
(2) Find the equation of line l that passes through point Q(0, -2) and intersects circle C at points A and B. The slopes of lines OA and OB are k₁ and k₂, respectively, where O is the coordinate origin and $k_{1}k_{2}=- \frac {1}{7}$.

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