
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 an ellipse C: $$\frac {x^{2}}{a^{2}} + \frac {y^{2}}{b^{2}} = 1$$ ($a > b > 0$) with an eccentricity of $$\frac {\sqrt {2}}{2}$$, and the area of the rhombus formed by its four vertices is $8\sqrt {2}$.  
(1) Find the equation of the ellipse;  
(2) Given a line $y=kx+m$ intersects the ellipse C at two distinct points A($x_1$, $y_1$) and B($x_2$, $y_2$), with O being the origin, and $k_{OA} \cdot k_{OB} = -\frac {1}{2}$, find the range of values for $y_1y_2$.

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