
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
Consider a hyperbola given by the equation $$\frac {x^{2}}{a^{2}}- \frac {y^{2}}{b^{2}}$$\=1 (a > 0, b > 0). Let F be its right focus. Draw a perpendicular line from F to one of the asymptotes, intersecting it at point A and the other asymptote at point B. If $$\overrightarrow {FB}$$\=2 $$\overrightarrow {FA}$$, find the eccentricity of this hyperbola.

A)  $$\frac {1}{2}$$
B) 2
C)  $$\sqrt {3}$$
D)  $$\sqrt {5}$$

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