
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
The ellipse $\dfrac{x^{2}}{a^{2}}+\dfrac{y^{2}}{b^{2}}=1 \left( a > b > 0 \right)$ and the circle $x^{2}+y^{2}=\left( \dfrac{b}{2}+c \right)^{2}$ (where $c$ is the semi-focal distance of the ellipse) have four distinct intersection points. The range of the eccentricity is \_\_\_\_\_\_\_\_

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