
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
$2.5$,$-0.5252252225\ldots$ (add a $2$ between every two $5$s),$-10^{2}$,$-5$,$0$,$\frac{1}{3}$,$|-4|$,$-3.6$,$\frac{π}{2}$.<br/>$(1)$Negative numbers:$\{ \_\_\_\_\_\_\ldots \}$;<br/>$(2)$Non-negative integers:$\{ \_\_\_\_\_\_\ldots \}$;<br/>$(3)$Fractions:$\{ \_\_\_\_\_\_\ldots \}$;<br/>$(4)$Irrational numbers:$\{ \_\_\_\_\_\_\ldots \}$.

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