
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
1. Using the enumeration method, represent the set: 
\[ A = \left\{ x \left\lvert\, x = \frac{a}{|a|} + \frac{|b|}{b} + \frac{|c|}{c} + \frac{a b c}{|a b c|} , \, a, b, c \in \mathbf{R}, \, a b c \neq 0 \right. \right\} \]

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