
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 sets for the following numbers: $-2$, $-3.14$, $0.3$, $0$, $\frac{π}{3}$, $\frac{22}{7}$, $-0.1212212221\ldots$ (with an increasing number of $2$ between each pair of $1$).<br/>$(1)$ Set of positive numbers: $\{ \_\_\_\_\_\_\ldots \ldots \}$;<br/>$(2)$ Set of negative numbers: $\{ \_\_\_\_\_\_\ldots \ldots \}$;<br/>$(3)$ Set of integers: $\{ \_\_\_\_\_\_\ldots \ldots \}$;<br/>$(4)$ Set of rational numbers: $\{ \_\_\_\_\_\_\ldots \ldots \}$.

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