
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 the center of the circle C lies on the positive x-axis and has a radius of 2, and the chord of circle C cut by the line y=$\sqrt{3}$x has a length of $\sqrt{13}$. <br /> (1) Find the equation of circle C; <br /> (2) Let the moving line y=k(x-2) intersect circle C at points A and B. Is there a fixed point N on the positive x-axis such that the lines AN and BN are symmetric about the x-axis? If so, find the coordinates of point N; if not, explain why.

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