
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 $\dfrac{x^{2}}{a^{2}} + \dfrac{y^{2}}{b^{2}} = 1 (a > b > 0)$ and a circle $x^{2} + y^{2} = \left(\dfrac{b}{2} + c\right)^{2}$, where $c$ is the semi-focal distance of the ellipse, and they intersect at four distinct points, find the range of the eccentricity $e$ of the ellipse.

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