
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
Suppose $a$ and $b$ are two distinct zero points of the function $f(x) = x^2 - px + q (p > 0, q > 0)$, and the numbers $a$, $b$, and $-2$ can be appropriately sorted to form an arithmetic sequence and a geometric sequence. Find the value of $p + q$.

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