
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
Given distinct real numbers \( p \) and \( q \), it is known that there exists a number \( x \) such that the following equalities are satisfied: \( x^2 + px + q = 0 \) and \( x^2 + qx + p = 0 \). What values can the sum \( p + q \) take?

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