
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 \( a^2 + b^2 = 1 \) (with \( b \neq 0 \)), if the line \( ax + by = 2 \) intersects the ellipse \( \frac{x^2}{6} + \frac{y^2}{2} = 1 \), determine the range of values for \( \frac{a}{b} \).

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