
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 that O is the coordinate origin, F is the left focus of the ellipse C: $$\frac {x^{2}}{a^{2}}+ \frac {y^{2}}{b^{2}}$$\=1 (a > b > 0), A, B, and D are the left, right, and top vertices of the ellipse C, respectively. P is a point on C, and PF is perpendicular to the x-axis. The line l passes through points A and D, intersecting the line PF at point M. If the line BM intersects the line segment OD at point N, and ON = 2ND, find the eccentricity of the ellipse C.

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