
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 two foci of the hyperbola $C$: $\frac{x^{2}}{a^{2}}- \frac{y^{2}}{b^{2}}=1 (a > 0, b > 0)$, and $M$, $N$ are two points on one asymptote of hyperbola $C$. If the quadrilateral $MF\_1NF\_2$ is a rectangle and $A$ is a vertex of the hyperbola, and the area of $\triangle AMN$ is $\frac{1}{2}c^{2}$, find the eccentricity of the hyperbola.

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