
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 $\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1 (a > b > 0)$ with its left and right foci being $F_1$ and $F_2$ respectively, and its eccentricity as $e$. If there exists a point $P$ on the ellipse such that $\dfrac{|PF_1|}{|PF_2|}=e$, then the range of the eccentricity $e$ is.

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