
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
Given that $a$ and $b$ are real numbers, consider the following statements: 
① If $ab \lt 0$ and $a$ and $b$ are opposite in sign, then $\frac{a}{b}=-1$; 
② If $a+b \lt 0$ and $ab \gt 0$, then $|2a+3b|=-2a-3b$; 
③ If $|a-b|+a-b=0$, then $b \gt a$; 
④ If $|a| \gt |b|$, then $\left(a+b\right)\times \left(a-b\right)$ is negative. Determine which statements are correct.

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