
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 an ellipse $\frac{x^2}{16} + \frac{y^2}{12} = 1$ whose right focus F lies at a distance less than $\sqrt{3}$ from the asymptote of the hyperbola $E: \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ (where $a > 0$, $b > 0$), determine the range of the eccentricity $e$ of the hyperbola $E$.

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