
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 moving point P in the plane and a fixed point N(0,1), the slope of the line connecting P and N is $k_1$, and the slope of the line connecting the midpoint of PN and the origin is $k_2$. It is known that $k_1k_2 = -\frac{1}{m^2}$ ($m > 1$), and the trajectory of point P is curve C.  
(1) Find the equation of curve C;  
(2) There exists exactly one circle that satisfies the following conditions simultaneously:  
① The diameter of the circle is a chord AB of curve C;  
② The circle passes through point N;  
③ The diameter $|AB| = \sqrt{2}|NB|$. Find the range of values for m.

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