
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 \( a \) and \( b \) be any real numbers. Consider the equation
\[ x^2 + |a| x + b = 0 \]
whose set of solutions in the complex numbers \(\mathbf{C}\) is \( A \). Define the set
\[ B = \{ n \mid n = |A|, a, b \in \mathbf{R} \} \]
Find the set \( B \).

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