
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 a hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ (where $a > 0, b > 0$), with one of its foci at F$(c, 0)$, and one endpoint of the imaginary axis at B$(0, b)$. If the line FB is perpendicular to the asymptote $y = \frac{b}{a}x$ of the hyperbola, find the eccentricity of this hyperbola.

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