
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 for the following numbers: $0.4$, $-\frac{2}{7}$, $\sqrt{5}$, $2023$, $-\sqrt{0.01}$, $-0.030030003\ldots$ (with an additional $0$ added between each two $3$s).

Positive number set: $\{ \_\_\_\_\_\_\ldots \}$;<br/>
Negative number set: $\{ \_\_\_\_\_\_\ldots \}$;<br/>
Rational number set: $\{ \_\_\_\_\_\_\ldots \}$;<br/>
Irrational number set: $\{ \_\_\_\_\_\_\ldots \}$.

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