
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 the right focus at \(F(c, 0)\), there exists a line \(l\) passing through point \(F\) that intersects the ellipse at points \(A\) and \(B\) such that \(OA \perp OB\). Find the range of the eccentricity of the ellipse.

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