
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 coefficients \( p \) and \( q \) of a quadratic equation \( x^{2} + px + q = 0 \) are each increased by one unit. This operation is repeated four times. Provide an example of such an initial equation such 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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