
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 quadratic function \( f(x) = x^2 + ax + b \) where \(a\) and \(b\) are real numbers, the function has two distinct zeros. If \( f(x^2 + 2x - 1) = 0 \) has four distinct roots \( x_1 < x_2 < x_3 < x_4 \) that form an arithmetic sequence, find the range of values for \(a - b\).

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