
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
Fill in the appropriate parentheses with the following numbers: $20$, $-4.8$, $0$, $-2023$, $+\frac{2}{7}$, $-\pi$, $0.020020002$, $0.010010001\ldots$, $0.1\overline{2}$.  
Negative number set: $\{ \_\_\_\_\_\_\ldots \}$;  
Fraction set: $\{ \_\_\_\_\_\_\ldots \}$;  
Non-positive integer set: $\{ \_\_\_\_\_\_\ldots \}$;  
Irrational number set: $\{ \_\_\_\_\_\_\ldots \}$.

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