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

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