
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 that {F}_{1} and {F}_{2} are the left and right foci of the ellipse \frac{{x}^{2}}{{a}^{2}}+\frac{{y}^{2}}{{b}^{2}}=1, and there is a point P on the line x=-a such that |PF_{1}|=|F_{1}F_{2}| and ∠PF_{1}F_{2}=120^{\circ}, find the eccentricity of the ellipse.

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