
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 with the equation $$\frac {x^{2}}{a^{2}}- \frac {y^{2}}{b^{2}}$$\=1 (a > b > 0), its right focus is F, and a line l passing through F intersects the asymptotes of the hyperbola at points A and B. The angle of inclination of line l is twice that of the asymptote OA. If $$\overrightarrow {AF}= \frac {5}{2} \overrightarrow {FB}$$, find the eccentricity of the hyperbola.

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