
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 a circle $O_{1}: x^{2}+y^{2}+2y-3=0$ and a fixed point $A(1, -2)$ inside it, $P$ and $Q$ are two different moving points on the circle.  
(1) If points $P$ and $Q$ are symmetric about a line $l$ passing through the fixed point $A$, find the equation of line $l$.  
(2) If the center $O_{2}$ of circle $O_{2}$ is symmetric to point $A$ about the line $x+3y=0$, and circle $O_{2}$ intersects circle $O_{1}$ at points $M$ and $N$, with $|MN|=2 \sqrt {2}$, find the equation of circle $O_{2}$.

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