
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
In the quadratic equation \(x^{2} + px + q = 0\), the coefficients \(p\) and \(q\) are increased by one. This operation is repeated four times. Provide an example of such an initial equation so that the roots of each of the five resulting equations are integers.

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