
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 equation of circle C, $(x^2 + (y-4)^2 = 4)$, and point O is the coordinate origin. Line $l: y=kx$ intersects circle C at points M and N.

(1) Find the range of values for k;
(2) Let Q(m, n) be a point on line segment MN such that $\frac{2}{|OQ|^2} = \frac{1}{|OM|^2} + \frac{1}{|ON|^2}$. Express n as a function of m.

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