
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
Let $Q(z) = z^3 + pz^2 + qz + r$, where $p, q,$ and $r$ are real numbers. Suppose a complex number $v$ exists such that the roots of $Q(z)$ are $v-2i$, $2v+2$, and $v+10i$. Determine the value of $p+q+r$.

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