
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 \(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 \ (a>b>0)\), which always passes through the point \(\left(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right)\), and the length of its major axis ranges from \(\sqrt{5}\) to \(\sqrt{6}\), determine the range of the eccentricity of the ellipse.

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