
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 two points M and N are symmetric about the line $y=k(x-1)$ and both lie on the circle $C: (x+3)^2+(y-4)^2=16$, and the line MN is tangent to the circle $x^2+y^2=2$, find the equation of the line MN.

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