
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
In the Cartesian coordinate system $xOy$, the ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1(a>b>0)$ has its right focus at $F(c, 0)$. If there is a line $l$ passing through the point $F$ that intersects the ellipse at points $A$ and $B$, such that $OA \perp OB$, find the range of values for the eccentricity $e=\frac{c}{a}$ of the ellipse.

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