
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
In the Cartesian coordinate system xOy, there is a circle O with the equation $x^2+y^2=4$ and a point P at $(-1,0)$. A line l passing through point P intersects circle O at points A and B.
(1) If $|AB|=2\sqrt{3}$, find the equation of line l.
(2) Let M be the midpoint of chord AB. Find the equation of the locus of point M.

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