
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 with the following numbers: $\frac{3}{5}$, $\sqrt{9}$, $\pi$, $3.14$, $-\sqrt[3]{27}$, $0$, $-5.12345\ldots$, $-\sqrt{3}$.

$(1)$ Set of rational numbers: $\{ \_\_\_\_\_\_\ldots \}$;<br/>$(2)$ Set of irrational numbers: $\{ \_\_\_\_\_\_\ldots \}$;<br/>$(3)$ Set of positive real numbers: $\{ \_\_\_\_\_\_\ldots \}$.

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