
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 point $F$ is the right focus of the hyperbola $\frac{x^{2}}{a^{2}}- \frac{y^{2}}{b^{2}}=1 (a > 0, b > 0)$, point $O$ is the coordinate origin, points $A$ and $B$ are located on the two asymptotes of the hyperbola respectively, $AF$ is perpendicular to the $x$-axis, $BF$ is parallel to $OA$, and $\overrightarrow{AB} \cdot \overrightarrow{OB} = 0$. Determine the eccentricity of the hyperbola.

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