
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 $(C)$: $x^{2}+2y^{2}=4$.
(I) Find the eccentricity of the ellipse $(C)$;
(II) Let $O$ be the origin. If point $A$ is on the line $y=2$, and point $B$ is on the ellipse $(C)$, and $OA \perp OB$, find the minimum length of line segment $AB$.

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