
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 M: $$\frac {x^{2}}{a^{2}}+ \frac {y^{2}}{b^{2}}=1(a>b>0)$$ with left and right foci $F_1$ and $F_2$ respectively. A focal chord perpendicular to the x-axis and passing through $F_2$ has a length of $$2 \sqrt {2}$$. A line 'l' passing through $F_1$ intersects ellipse M at points G and H, and the perimeter of △GH$F_2$ is $$8 \sqrt {2}$$.

1. Find the equation of the ellipse M.
2. Given that lines $l_1$ and $l_2$ are perpendicular to each other, line $l_1$ passes through $F_1$ and intersects ellipse M at points A and B, and line $l_2$ passes through $F_2$ and intersects ellipse M at points C and D. Find the value of $$\frac {1}{|AB|}+ \frac {1}{|CD|}$$.

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