
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 points $A$ and $B$ with coordinates $(0,-1)$ and $(0,1)$ respectively, lines $AM$ and $BM$ intersect at point $M$, and the product of their slopes is $- \frac {1}{2}$.  
$(1)$ Find the equation of the trajectory $C$ of point $M$;  
$(2)$ If a line $l$ passing through point $D(0,2)$ intersects the trajectory $C$ from $(1)$ at two distinct points $E$ and $F$, find the range of the area of $\triangle OEF$ ($O$ is the origin).

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