
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 sets with the following numbers: $-|-2.5|$, $0$, $-(-5^{2})$, $+(-\frac{1}{3})^{2}$, $-1.2121121112\ldots$, $-\frac{3}{4}$, $\pi$.  
Set of positive numbers: $\{ \_\_\_\_\_\_\ldots \}$  
Set of integers: $\{ \_\_\_\_\_\_\ldots \}$  
Set of negative fractions: $\{ \_\_\_\_\_\_\ldots \}$  
Set of irrational numbers: $\{ \_\_\_\_\_\_\ldots \}$.

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