
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 $\frac{x^{2}}{a^{2}}+ \frac{y^{2}}{b^{2}}=1$ $(a > b > 0)$ and a point $A$ on it, let $B$ be the symmetric point of $A$ with respect to the origin, and $F$ be its left focus. If $AF \perp BF$, and let $\angle ABF = \theta$, with $\theta \in [\frac{\pi}{6}, \frac{\pi}{3}]$, find the range of the eccentricity $e$ of the ellipse.

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