
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, the origin of the coordinates. Line l, defined as $y=kx$, intersects circle C at points M and N.

(I) Find the range of k;

(II) Let Q(m,n) be a point on 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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