
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: $(x+1)^2+y^2=4$ and a point outside the circle A$(1, 2\sqrt{3})$,  
(1) If line $m$ passes through the origin $O$ and exactly three points on circle $C$ are at a distance of 1 from line $m$, find the equation of line $m$;  
(2) If a line $l$ passing through $A$ is tangent to circle $C$ at points $D$ and $E$, find the equations of the tangent lines and the line on which $D$ and $E$ lie.

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