
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 the line l: $$x+y+4 \sqrt {2}=0$$, a circle C with a radius of 4 is tangent to the line l. The center of the circle C is on the x-axis and is located on the right upper side of the line l.
(1) Find the equation of circle C;
(2) A line passing through point M(2,0) intersects circle C at points A and B (A is above the x-axis). Does there exist a fixed point N on the positive half of the x-axis such that the x-axis bisects angle ANB? If it exists, find the coordinates of point N; if not, explain the reason.

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