
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 that $F\_1(-c,0)$ and $F\_2(c,0)$ are the two foci of the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 (a > b > 0)$, if there exists a point $P$ on the ellipse such that $\overrightarrow{PF_1} \cdot \overrightarrow{PF_2} = 2c^2$, then the range of the eccentricity of this ellipse is.

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