
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 coordinates of points A and B are (0, -1) and (0, 1) respectively, the 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, determine the range of the area of $\triangle OEF$ (where O is the origin of the coordinates).

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