
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
An ellipse C is defined by the equation $$\frac {x^{2}}{a^{2}}+ \frac {y^{2}}{b^{2}}=1$$ (a > b > 0), and its four vertices form a rhombus with side length $$\sqrt {3}$$ and area $$2 \sqrt {2}$$.
(1) Find the equation of ellipse C.
(2) A line l passes through point Q(0, -2) and intersects ellipse C at points A and B. If the product of the slopes of OA and OB (where O is the origin) is -1, find the length of segment AB.

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