
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 $\frac {x^{2}}{a^{2}}+ \frac {y^{2}}{b^{2}}=1(a>b>0)$ with left and right foci $F_1$ and $F_2$ respectively, and eccentricity $e$, if there exists a point $P$ on the ellipse such that $\frac {PF_{1}}{PF_{2}}=e$, then the range of the eccentricity $e$ is ________.

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