
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 $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$ $(a > b > 0)$ with its right focus at $F_{2}(3,0)$ and eccentricity $e$.

(Ⅰ) If $e=\frac{\sqrt{3}}{2}$, find the equation of the ellipse;

(Ⅱ) Let the line $y=kx$ intersect the ellipse at points $A$ and $B$, with $M$ and $N$ being the midpoints of segments $AF_{2}$ and $BF_{2}$, respectively. If the origin $O$ lies on the circle with diameter $MN$, and $\frac{\sqrt{2}}{2} < e \leqslant \frac{\sqrt{3}}{2}$, find the range of values for $k$.

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