
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 F<sub>1</sub> and F<sub>2</sub> are the left and right foci of the ellipse \\(\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 (a > b > 0)\\), a line passing through F<sub>2</sub> and perpendicular to the x-axis intersects the ellipse at points A and B. If triangle ∆ABF<sub>1</sub> 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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