
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
The following statements: ① If $|x|+x=0$, then $x$ is a negative number; ② If $-a$ is not a negative number, then $a$ is a non-positive number; ③ $|-a^{2}|=\left(-a\right)^{2}$; ④ If $\frac{a}{|a|}+\frac{b}{|b|}=0$, then $\frac{ab}{|ab|}=-1$; ⑤ If $|a|=-b$, $|b|=b$, then $a=b$. The correct conclusions are ______. (Fill in the numbers)

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