
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 ellipse $\dfrac{x^{2}}{16} + \dfrac{y^{2}}{12} = 1$ and its right focus $F$, if the distance from $F$ to the asymptote of the hyperbola $E$: $\dfrac{x^{2}}{a^{2}} - \dfrac{y^{2}}{b^{2}} = 1$ $(a > 0, b > 0)$ is less than $\sqrt{3}$, then the range of the eccentricity $e$ of the hyperbola $E$ is ______.

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