
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 $\frac{x^{2}}{2}+y^{2}=1$ with its right focus $F$, a line $l$ intersects the ellipse at two points $C$ and $D$, and intersects the line $x=2$ at point $E$.
(I) If the slope of line $l$ is $2$, find the length of segment $|CD|$.
(II) Let $O$ be the coordinate origin. If $S_{\triangle ODE}:S_{\triangle OCE}=1:3$, find the equation of line $l$.

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