
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 $W$: $\frac{x^2}{2}+y^2=1$, and $O$ is the origin. <br/>$(Ⅰ)$ When point $B$ is the right vertex of the ellipse $W$, and quadrilateral $OABC$ is a rhombus, find the area of this rhombus; <br/>$(Ⅱ)$ The line passing through the right focus $F$ intersects the ellipse at points $A$ and $B$, with point $M(0,m)$, if $|MA|=|MB|$, find the range of real number $m$.

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