
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 the equation of circle C: $x^{2}+y^{2}=4$.
(1) Find the equation of the line l that is tangent to circle C and passes through point P(1,2).
(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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