
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
Find all integer pairs \((a, b)\) such that there exists a polynomial with integer coefficients \( p(x) \) satisfying that the product \((x^{2} + ax + b)p(x)\) has the form \(x^n + c_{n-1}x^{n-1} + \cdots + c_0\), where each \( c_i \) is either 1 or -1.

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