
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 the following 4 propositions:  
① If the graph of a function intersects with the graph of its inverse function, then the intersection point must be on the line $y=x$;  
② The graph of the function $y=f(1-x)$ is symmetric to the graph of the function $y=f(1+x)$ about the line $x=1$;  
③ If the graph of an odd function $y=f(x)$ is symmetric about the line $x=a$, then the period of $y=f(x)$ is $2a$;  
④ Given the sets $A=\{1,2,3\}$, $B=\{4,5\}$, then there are 8 functions with $A$ as the domain and $B$ as the codomain.  
Among the above four propositions, the numbers of all incorrect propositions are.

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