
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 ellipse $C$: $\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1 (a > b > 0)$ have its left and right foci as $F_1$ and $F_2$, respectively. A perpendicular line to the $x$-axis passing through $F_2$ intersects $C$ at points $A$ and $B$. The line $F_1B$ intersects the $y$-axis at point $D$. If $AD \perpendicular F_1B$, then the eccentricity of ellipse $C$ equals \_\_\_\_\_\_\_\_.

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