
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 the left focus of the ellipse $\frac{{x}^{2}}{{a}^{2}}+ \frac{{y}^{2}}{{b}^{2}}=1$ $(a > b > 0)$ is ${{F}\_{1}}$, a line passing through ${{F}\_{1}}$ with a slope angle of $30{}^\circ$ intersects the circle ${{x}^{2}}+{{y}^{2}}={{b}^{2}}$. The length of the chord formed by the intersection is $\sqrt{2}b$. Find the eccentricity of the ellipse.

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