
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
Let the right directrix of the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ ($a > b > 0$) intersect the x-axis at point M. A circle O is drawn with the major axis of the ellipse as its diameter. A tangent line to circle O passing through point M touches the circle at point N. If $\triangle OMN$ is an isosceles right triangle, then the eccentricity of the ellipse is $\boxed{\sqrt{2} - 1}$.

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