
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
Given the following real numbers:①$-\frac{1}{2}$ ②$\sqrt{5}$ ③$\frac{π}{3}$ ④$3.14$ ⑤$\frac{23}{7}$ ⑥$0$ ⑦$-\sqrt{16}$ ⑧$1.323323332\ldots$ (with an increasing number of $3$ between every two $2$) (only fill in the numbers). The integers are: _______, the fractions are: _______, and the irrational numbers are: _______.

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