
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 with equation $$\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$$ with a > b > 0, the left and right foci are F1 and F2 respectively, O is the coordinate origin, A is a point on the ellipse, and $$\overrightarrow{AF_{1}} \cdot \overrightarrow{AF_{2}} = 0$$, if the line AF2 intersects the y-axis at point M and |F1F2| = 6|OM|, calculate the eccentricity of the ellipse.

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