
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
Among the following four propositions:  
① If the inverse of a proposition is true, then its contrapositive must also be true;  
② The proposition "Let $a, b \in \mathbb{R}$, if $a+b \neq 6$, then $a \neq 3$ or $b \neq 3$" is false;  
③ "$x > 2$" is a sufficient but not necessary condition for "$\frac{1}{x} < \frac{1}{2}$";  
④ If the negation of a proposition is true, then its inverse must also be true.  
The incorrect propositions are \_\_\_\_\_\_ . (Write down the numbers of all incorrect propositions)

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