
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 $F$ is the right focus of the hyperbola $\dfrac {x^{2}}{a^{2}}- \dfrac {y^{2}}{b^{2}}=1 (a > 0, b > 0)$, point $A$ is a vertex on the imaginary axis of the hyperbola, and the line passing through $F$ and $A$ intersects with one asymptote of the hyperbola at point $B$ on the left side of the $y$-axis. If $\overrightarrow{FA}=( \sqrt {2}-1) \overrightarrow{AB}$, calculate the eccentricity of this hyperbola.

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