
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 $A$, $B$, $C$ are three points on the ellipse $W$: $x^{2}+2y^{2}=2$, and $O$ is the coordinate origin.
(I) If the equation of the line containing $A$ and $C$ is $y=x+1$, find the length of $AC$;
(II) Suppose $P$ is a point on the line segment $OB$, and $|OB|=3|OP|$, determine whether the area of $\triangle OAC$ is a constant when the midpoint of $AC$ is exactly at point $P$.

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