
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
In the Cartesian coordinate system $xOy$, the circle $C$: $x^{2}+y^{2}+4x-2y+m=0$ is tangent to the line $x- \sqrt {3}y+ \sqrt {3}-2=0$.  
(Ⅰ) Find the equation of circle $C$;  
(Ⅱ) If there are two points $M$, $N$ on circle $C$ that are symmetric with respect to the line $x+2y=0$, and $|MN|=2 \sqrt {3}$, find the equation of line $MN$.

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