
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 \( Q(z) = z^3 + az^2 + bz + c \), where \( a, b, \) and \( c \) are real numbers. There exist a complex number \( u \) such that the three roots of \( Q(z) \) are \( u + 5i \), \( u + 15i \), and \( 2u - 6 \), where \( i^2 = -1 \). Find \( a + b + c \).

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