
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 N with center (3, 4), its radius is equal to the distance between two parallel lines \((a-2)x+y+ \sqrt {2}=0\) and \(ax+3y+2 \sqrt {2}a=0\).
(1) Find the equation of circle N;
(2) Point B(3, -2) is symmetrical to point C with respect to the line \(x=-1\). Find the equation of the circle with center C that is tangent to circle N.

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