
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 the hyperbola C: $$\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 (a > 0, b > 0)$$ with its left focus as F, the line x = c (where c is the semi-major axis) intersects the asymptotes of C at points A and B. If triangle FAB is an isosceles right triangle, what is the eccentricity of C?

A) 2
B) $$\sqrt{2}$$
C) $$\sqrt{5}$$
D) $$\frac{1 + \sqrt{5}}{2}$$

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