
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: $x^2+y^2-4x+3=0$.
(1) Find the value of $m$ for the line $l$ passing through point $P(1,2)$ with slope $m$ that is tangent to circle C.
(2) Line $a$ passes through point $Q(0,-2)$ intersecting circle C at points A and B. The slopes of lines OA and OB are $k_1$ and $k_2$, respectively, where O is the coordinate origin and $k_1k_2=-\frac{1}{7}$. Find the equation of line $a$.

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