
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 $P$ is a fixed point on an ellipse, $F\_1$ and $F\_2$ are the two foci of the ellipse. If $\angle PF\_1F\_2 = 60^{\circ}$ and $|PF\_2| = \sqrt{3}|PF\_1|$, what is the eccentricity of the ellipse?

A) $\frac{\sqrt{3}-1}{2}$
B) $\sqrt{3}-1$
C) $2-\sqrt{3}$
D) $1-\frac{\sqrt{3}}{2}$

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