
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: $-\frac{1}{2}$, $2\sqrt{2}$, $\sqrt[3]{-64}$, $0.26$, $\frac{π}{7}$, $0.10$, $5$.$\stackrel{．}{1}\stackrel{．}{2}$, $|\sqrt[3]{-3}|$, $3+\sqrt{27}$.<br/>$(1)$ Set of rational numbers: $\{ \_\_\_\_\_\_\ldots \}$;<br/>$(2)$ Set of irrational numbers: $\{ \_\_\_\_\_\_\ldots \}$.

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