
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 that the endpoint B of the line segment AB has coordinates (0, 3), and endpoint A moves on the circle C: $(x+1)^2+y^2=4$.  
(1) Find the equation of the trajectory of the midpoint M of line segment AB;  
(2) A line $l$ passing through point B intersects circle C at two points A and B, and the length of chord AB is $\frac{2\sqrt{19}}{5}$. Find the equation of line $l$.

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