
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 ellipse \(\frac{x^{2}}{6}+\frac{y^{2}}{2}=1\) with the right focus at \(F\), a line passing through \(F\) of the form \(y=k(x-2)(k \neq 0)\) intersects the ellipse at points \(P\) and \(Q\). If the midpoint of \(PQ\) is \(N\), \(O\) is the origin, and the line \(ON\) intersects the line \(x=3\) at point \(M\), find:
(1) The measure of \(\angle M F Q\);
(2) The maximum value of \(\frac{P Q}{M F}\).

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