
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
An ellipse is given by the equation $\frac{x^{2}}{a^{2}}+ \frac{y^{2}}{b^{2}}=1$ $(a > b > 0)$. Let $F\_1$ be the left focus of the ellipse and $F\_2$ be the right focus. Draw a perpendicular line from $F\_1$ to the $x$-axis that intersects the ellipse at point $P$. If the angle $\angle F\_1PF\_2 = 60^\circ$, find the eccentricity of the ellipse.

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

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