
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 propositions:  
① 0 is greater than $-i$;  
② Two complex numbers are conjugates of each other if and only if their sum is a real number;  
③ The necessary and sufficient condition for $x+yi=1+i$ is $x=y=1$;  
④ If we associate the real number $a$ with $ai$, then there is a one-to-one correspondence between the set of real numbers and the set of pure imaginary numbers;  
⑤ Let $z$ be a complex number, then $|z|^2=|\overline{z}|^2=z\cdot\overline{z}$.  
The correct ones are \_\_\_\_\_\_ .

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