
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 two of the roots of the cubic equation \[ax^3 + bx^2 + cx + d = 0\] are \(1 + i\) and \(1 - i\), and \(a \neq 0\), compute \(\frac{b + c}{a}\).

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