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

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