
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 points $F_1$ and $F_2$ are the left and right foci of the ellipse $\frac{x^{2}}{a^{2}}+ \frac{y^{2}}{b^{2}}=1 (a > b > 0)$, find the eccentricity of the ellipse given that there exists a point $P$ on the ellipse such that $\angle F_1PF_2=60^{\circ}$ and $|PF_1|=2|PF_2|$.

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