
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 corresponding braces with the following numbers: $-3$, $+\left(-1\right)$, $0$, $20$, $\frac{1}{4}$, $-6.5$, $17\%$, $-8\frac{1}{2}$, $-\left(-7\right)$, $\pi$, $\left(-4\right)^{2}$, $-|-3.14|$.  
Set of positive numbers: $\{ \_\_\_\_\_\_\ldots \}$;  
Set of integers: $\{ \_\_\_\_\_\_\ldots \}$;  
Set of fractions: $\{ \_\_\_\_\_\_\ldots \}$;  
Set of positive integers: $\{ \_\_\_\_\_\_\ldots \}$;  
Set of non-negative rational numbers: $\{ \_\_\_\_\_\_\ldots \}$.

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