
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 C: $$\frac {x^{2}}{a^{2}}$$ - $$\frac {y^{2}}{b^{2}}$$ = 1 (a > 0, b > 0), and the line y = $$\sqrt {3}$$x intersects C at points A and B, with AF perpendicular to BF, determine the eccentricity of C.

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