
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 the left and right foci of the hyperbola $\dfrac {x^{2}}{a^{2}} - \dfrac {y^{2}}{b^{2}} = 1 (a > 0, b > 0)$ be $F_{1}$ and $F_{2}$, respectively. A circle centered at $F_{2}$ with radius $|F_{1}F_{2}|$ intersects the hyperbola in the first and second quadrants at points $A$ and $B$, respectively. If $3|F_{1}B| = |F_{2}A|$, find the eccentricity of the hyperbola.

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