
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
The function  $f(x) = x^2+ax+b$  has two distinct zeros. If  $f(x^2+2x-1)=0$  has four distinct zeros  $x_1<x_2<x_3<x_4$  that form an arithmetic sequence, compute the range of  $a-b$ .

*(Source: China National High School Mathematics League 2021, Zhejiang Province, Problem 11)*

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