
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 triangle $ABC$, it is known that the equation of the line containing the height from $AB$ is $l_1: x+3y+2=0$, the equation of the line containing the angle bisector of $\angle C$ is $l_2: y-2=0$, and the coordinates of point $A$ are $(0, -2)$. Find:  
(1) The coordinates of point $C$;  
(2) The equation of line $AB$;  
(3) The equation of line $BC$.

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