
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 a circle with center at point $A\left(-1,2\right)$ is tangent to the line $m:x+2y+7=0$, and the moving line $l$ passing through point $B\left(-2,0\right)$ intersects the circle $A$ at points $M$ and $N$.

(I) Find the equation of circle $A$;

(II) When $\left|MN\right|=2\sqrt{19}$, find the equation of line $l$.

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