
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 $C$: $\frac{x^{2}}{a^{2}}+ \frac{y^{2}}{b^{2}}=1(a > b > 0)$ with two foci $F_{1}(-2,0)$, $F_{2}(2,0)$, and an eccentricity of $\frac{\sqrt{6}}{3}$. A line $l$ (with a slope not equal to $0$) passes through focus $F_{2}$ and intersects the ellipse $C$ at points $A$ and $B$. The midpoint of segment $AB$ is $D$, and $O$ is the coordinate origin. The line $OD$ intersects the ellipse at points $M$ and $N$.

(I) Find the equation of ellipse $C$;

(II) When the quadrilateral $MF_{1}NF_{2}$ is a rectangle, find the equation of line $l$.

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