
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 the hyperbola $C: \frac {x^{2}}{a^{2}} - \frac {y^{2}}{b^{2}} = 1$ with its right focus at $F(c,0)$, and the line $x=a$ intersects the asymptote of hyperbola $C$ in the first quadrant at point $A$. Let $O$ be the origin. If the area of triangle $OAF$ is $\frac {3}{16}a^{2}$, determine the eccentricity of the hyperbola $C$.

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