
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 $Q(z) = x^3 + ax^2 + bx + c$, where $a$, $b$, and $c$ are real coefficients. Suppose there exists a complex number $u$ such that the roots of $Q(z)$ are $u + 2i$, $u - 2i$, and $2u + 3$. Find $a + b + c$.

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