
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 points $F_1$ and $F_2$ are the left and right foci of the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ $(a > b > 0)$, respectively, a line passing through $F_1$ perpendicular to the $x$-axis intersects the ellipse at points $A$ and $B$. If $\triangle ABF_2$ is an acute triangle, determine the range of the eccentricity $e$ of the ellipse.

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