
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 blanks with the following numbers: $0$.$\stackrel{••}{12}$, $0$, $-9$, $-6.8$, $2-\pi$, $\frac{13}{9}$, $-\sqrt{2}$, $80\%$, $\sqrt[3]{729}$, $0.7373373337\ldots$ (with one more "3" between every two "7"s), $\sqrt{(-3)^2}$.  
Irrational numbers: $\{ \_\_\_\_\_\_\ldots \}$;  
Integers: $\{ \_\_\_\_\_\_\ldots \}$;  
Fractions: $\{ \_\_\_\_\_\_\ldots \}$;  
Real numbers: $\{ \_\_\_\_\_\_\ldots \}$.

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