
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
The endpoint of the imaginary axis of a hyperbola is $M$, and its two foci are $F\_1$ and $F\_2$, respectively, with $\angle F\_1MF\_2 = \frac{2\pi}{3}$. Determine the eccentricity of the hyperbola.

A) $\sqrt{3}$
B) $\frac{\sqrt{6}}{2}$
C) $\frac{\sqrt{5}}{3}$
D) $\frac{\sqrt{3}}{3}$

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