
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 the equation $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ $(a > b > 0)$, its major axis is divided into three equal parts by the two intersection points of the circle $x^2 + y^2 = b^2$ and the $x$-axis. What is the eccentricity of the ellipse?

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