
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
Classify the following numbers (just fill in the numbers).<br/>①$\sqrt[3]{-8}$; ②$0.3$; ③$0$; ④$\sqrt{7}$; ⑤$0.3030030003\ldots$ (with one more $0$ between each pair of $3$); ⑥$-\frac{3}{7}$.<br/>Integers: ______; <br/>Fractions: ______; <br/>Irrational numbers: ______.

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