
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 E: $$\frac {x^{2}}{a^{2}}$$+ $$\frac {y^{2}}{b^{2}}$$\=1 (a＞b＞0) with left and right foci $F_1$ and $F_2$ respectively. The ellipse passes through the point (0, 2), and point Q is a moving point on the ellipse (distinct from the left and right vertices) such that the perimeter of △$QF_1F_2$ is 4+4 $$\sqrt {2}$$.

1. Find the equation of ellipse E.
2. Draw lines $l_1$ and $l_2$ with slopes $k_1$ and $k_2$ passing through points $F_1$ and $F_2$ respectively, intersecting ellipse E at points A, B and C, D respectively. Given that |AB|+|CD|=6 $$\sqrt {2}$$, find the value of $k_1k_2$.

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