
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 > 0, b > 0), let F1 and F2 be its left and right foci, respectively. P is a point on the hyperbola such that the distance from P to the center of the hyperbola is equal to half of the focal distance, and |PF1| + |PF2| = 4a. Determine the eccentricity of the hyperbola.

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