
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: $x^2+y^2=4$.  
(I) 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 $l$;  
(II) A line $m$, parallel to the x-axis, is drawn through a moving point M on circle C. Let N be the intersection of $m$ and the y-axis. If vector $\overrightarrow{OQ} = \overrightarrow{OM} + \overrightarrow{ON}$, find the trajectory equation of point Q and explain what curve this trajectory is.

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