
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 the line $y=\frac{2 \sqrt{3}}{3} x$ and the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1(a>b>0)$ intersect at two distinct points $M$ and $N$, if the projections of $M$ and $N$ on the $x$-axis are exactly the two foci of the ellipse, find the eccentricity of the ellipse.

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