
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 a major axis length of 2$$\sqrt {2}$$. P is a moving point on the ellipse C, distinct from the vertices, O is the coordinate origin, A₂ is the right vertex of the ellipse C, M is the midpoint of the line segment PA₂, and the product of the slopes of the lines PA₂ and OM is -$$\frac {1}{2}$$.

1. Find the equation of ellipse C.
2. A line l passes through the left focus F₁ of ellipse C and intersects the ellipse C at two points A and B. The perpendicular bisector of line segment AB intersects the x-axis at point N. The range of the x-coordinate values of point N is $$(- \frac {1}{4}，0)$$. Find the range of the length of line segment AB.

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