
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 \(F_{1}\) and \(F_{2}\) are the two focal points of the hyperbola \( \frac {x^{2}}{a^{2}} - \frac {y^{2}}{b^{2}} = 1 \), if there exists a point \(P\) on the hyperbola such that the angle \(∠F_{1}PF_{2}\) equals \( \frac {2π}{3} \), and \(|F_{1}P| = 3|PF_{2}|\), then the eccentricity of the hyperbola is _______.

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