
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 $E$: $\frac{x^{2}}{a^{2}}+ \frac{y^{2}}{b^{2}}=1(a > b > 0)$ with a focal length of $2c(c > 0)$, the left focus is $F$, and the coordinates of point $M$ are $(-2c,0)$. If there exists a point $P$ on ellipse $E$ such that $|PM|= \sqrt {2}|PF|$, then the range of the eccentricity of ellipse $E$ is _____.

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