
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
The eccentricity of the hyperbola defined by the equation $\frac {x^{2}}{a^{2}} - \frac {y^{2}}{b^{2}} = 1$ given that a line with a slope of -1 passes through its right vertex A and intersects the two asymptotes of the hyperbola at points B and C, and if $\overrightarrow {AB}= \frac {1}{2} \overrightarrow {BC}$, determine the eccentricity of this hyperbola.

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