
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
If \( a \pm b \mathrm{i} \) \( (b \neq 0) \) is an imaginary root of the equation \( x^{3} + qx + r = 0 \), where \( a, b, q \), and \( r \) are all real numbers, then \( q \) can be expressed in terms of \( a \) and \( b \) as _______.


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