
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
If $a$ and $b$ are two distinct roots of the function $f(x) = x^2 - px + q$ ($p > 0$, $q > 0$), and $a$, $b$, $-2$ can form an arithmetic sequence after being arranged in some order, and also form a geometric sequence after being arranged in another order, calculate the value of $a+b$.

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