
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 $C$: $x^{2}+y^{2}=4$.
(1) Find the equation of the tangent line passing through point $M(4,0)$;
(2) Line $l$ passes through point $P(1,2)$, and intersects circle $C$ at points $A$ and $B$. If $|AB|=2 \sqrt {3}$, find the equation of line $l$.

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