
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 quadratic function \(y=f(x)\) has a leading coefficient of 1. The coefficients of the linear term and the constant term are integers. Given that \(f(f(x))=0\) has four distinct real roots, and these roots can be arranged in an arithmetic sequence, find the function \(f(x)\) such that the sum of its coefficients is minimized.

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