
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 \(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\) where \(a > b > 0\) always passes through the fixed point \(\left(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right)\), and the range of lengths for its major axis is \([\sqrt{5}, \sqrt{6}]\). What is the range of values for its eccentricity?

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