
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
Write the following numbers into the corresponding sets: $-\frac{1}{10}$, $\sqrt[3]{8}$, $0.3$, $-\frac{π}{3}$, $-\sqrt{64}$, $0$, $\sqrt{0.9}$, $\frac{22}{7}$.  
Set of positive fractions $\{ \_\_\_\_\_\_\ldots \}$;  
Set of integers $\{ \_\_\_\_\_\_\ldots \}$;  
Set of irrational numbers $\{ \_\_\_\_\_\_\ldots \}$.

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