
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 numbers for the following numbers.<br/>①$0$, ②$\sqrt{5}$, ③$-3.5$, ④$\pi $, ⑤$-\frac{12}{7}$, ⑥$\sqrt[3]{-27}$, ⑦$|-8|$, ⑧$1.202002\cdots$ (with one more "0" between every two "2"s).<br/>$(1)$ Positive integers: ______; <br/>$(2)$ Negative fractions: ______; <br/>$(3)$ Irrational numbers: ______.

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