
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
A certain quadratic trinomial \(x^{2}-p x+q\) has integer roots \(x_{1}\) and \(x_{2}\). It turns out that the numbers \(x_{1}\), \(x_{2}\), and \(q\) form a decreasing arithmetic progression. Find the sum of the possible values of \(x_{2}\).

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