
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 that point $F$ is the left focus of the hyperbola $\frac{x^2 }{a^2 } - \frac{y^2 }{b^2 } = 1 (a > 0, b > 0)$, and point $E$ is the right vertex of the hyperbola. The line passing through $F$ and perpendicular to the $x$-axis intersects the hyperbola at points $A$ and $B$. If $\triangle ABE$ is an acute triangle, then the range of the eccentricity $e$ of the hyperbola is _______.

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