
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 appropriate parentheses with the following numbers: $-8$, $-0.275$, $\frac{22}{7}$, $0$, $-(-10)$, $-1.4040040004\ldots$, $-\frac{1}{3}$, $-(+2)$, $\frac{\pi}{3}$, $0.5$.

Positive number set $\left\{\_\_\_\ldots \right\}$;

Irrational number set $\left\{\_\_\_\ldots \right\}$;

Integer set $\left\{\_\_\_\ldots \right\}$;

Negative fraction set $\left\{\_\_\_\ldots \right\}$.

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