
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 $A(-1, 2)$ is tangent to the line $l_{1}$: $x + 2y + 7 = 0$, and a moving line $l$ passing through point $B(-4, 0)$ intersects with circle $A$ at points $M$ and $N$.
(1) Find the equation of circle $A$;
(2) Find the equation of line $l$ when $|MN| = 2\sqrt{11}$.

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