
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 is: $x^2+y^2=4$

(1) Find the equation of line $l$ that passes through point P(2, 1) and is tangent to circle C;  
(2) Line $l$ passes through point D(1, 2), and intersects circle C at points A and B. If $|AB|=2\sqrt{3}$, find the equation of line $l$;  
(3) On circle C, there is a moving point M($x_0$, $y_0$), $\overrightarrow{ON}=(0, y_0)$, if vector $\overrightarrow{OQ}=\overrightarrow{OM}+\overrightarrow{ON}$, find the trajectory equation of moving point Q.

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