
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 $Q(z) = x^3 + px^2 + qx + r$, where $p$, $q$, and $r$ are real numbers. There exists a complex number $w$ such that the roots of $Q(z)$ are $w+4i$, $w+10i$, and $3w-5$. Determine the value of $p+q+r$.

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