
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 arbitrary real numbers. The equation \( x^{2} + a|x| + b = 0 \) has a set of solutions \( \text{A} \) in the complex number set \( \mathbb{C} \). If \( |\mathbf{A}| = n \), determine the set of all possible values of \( n \), forming the set \( B \).

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