
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 points $A(-3,0)$ and $B(1,0)$, where line segment $AB$ is the diameter of circle $M$.  
$(Ⅰ)$ Find the equation of circle $M$;  
$(Ⅱ)$ A line $l$ passing through point $(0,2)$ intersects circle $M$ at points $D$ and $E$, where $|DE|=2\sqrt{3}$. Find the equation of line $l$.

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