
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 the right focus of the hyperbola $\dfrac {x^{2}}{a^{2}} - \dfrac {y^{2}}{b^{2}} = 1 (a > 0, b > 0)$ be $F$. A line $l$ perpendicular to the $x$-axis and passing through point $F$ intersects the two asymptotes at points $A$ and $B$, and intersects the hyperbola in the first quadrant at point $P$. Let $O$ be the origin. If $\overrightarrow{OP} = \lambda \overrightarrow{OA} + \mu \overrightarrow{OB} (\lambda, \mu \in \mathbb{R})$ and $\lambda\mu = \dfrac {3}{16}$, find the eccentricity of the hyperbola.

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