
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
Let $F_{1}$ and $F_{2}$ be the two foci of the hyperbola $C$: $\dfrac {x^{2}}{a^{2}}- \dfrac {y^{2}}{b^{2}}=1$ ($a > 0$, $b > 0$), and let $M$, $N$ be two points on one of the asymptotes of the hyperbola $C$. The quadrilateral $MF_{1}NF_{2}$ is a rectangle, and $A$ is a vertex of the hyperbola. If the area of $\triangle AMN$ is $\dfrac {1}{2}c^{2}$, determine the eccentricity of this hyperbola.

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