
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 hyperbola C: $$\frac {x^{2}}{a^{2}}- \frac {y^{2}}{b^{2}}$$\=1 (a, b > 0), and A is the left vertex of the hyperbola. A circle with $F\_1 F\_2$ as the diameter intersects one of the asymptotes of the hyperbola at points M and N, such that ∠MAN = 120°. Determine the eccentricity of the hyperbola.

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