
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 that the right focus of the ellipse $\frac{x^{2}}{a^{2}}+ \frac{y^{2}}{b^{2}}=1(a > b > 0)$ is $F_{2}(3,0)$, and the eccentricity is $e$.
(I) If $e= \frac{ \sqrt {3}}{2}$, find the equation of the ellipse;
(II) If the line $y=kx(k > 0)$ intersects the ellipse at points $A$ and $B$, and $\overrightarrow{AF_{2}} \cdot \overrightarrow{BF_{2}}=0$, with $\frac{ \sqrt {2}}{2} < e \leqslant \frac{ \sqrt {3}}{2}$, find the minimum value of $k$.

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