
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 M whose distance to the point (8, 0) is twice its distance to the point (2, 0).  
(1) Find the equation of the trajectory C of the moving point M;  
(2) If the line $y=kx-5$ has no intersection with trajectory C, find the range of values for $k$;  
(3) Given that the circle $x^2+y^2-8x-8y+16=0$ intersects trajectory C at points A and B, find $|AB|$.

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