
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 that $a$ and $b$ are two distinct roots of the function $f(x)=x^{2}-px+q$ ($p > 0,q > 0$), and the three numbers $a$, $b$, and $-4$ can be arranged in ascending or descending order to form both an arithmetic and a geometric sequence, calculate the value of $p+q$.

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