
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 $C$: $\dfrac{x^{2}}{a^{2}} + \dfrac{y^{2}}{b^{2}} = 1 (a > b > 0)$, where the left and right foci are $F_{1}$ and $F_{2}$ respectively, the right vertex is $A$, and the top vertex is $B$. Calculate the eccentricity $e$ of the ellipse $C$ if the distance from the center of the ellipse $C$ to the line $AB$ is $\dfrac{\sqrt{6}}{6}|F_{1}F_{2}|$.

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