
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
For non-zero real numbers $a$ and $b$, the following four propositions all hold:  
① $$a+ \frac {1}{a} \neq 0$$; ② $(a+b)^2 = a^2 + 2ab + b^2$;  
③ If $|a| = |b|$, then $a = \pm b$; ④ If $a^2 = ab$, then $a = b$.  
Then, for non-zero complex numbers $a$ and $b$, the propositions that still hold are \_\_\_\_\_\_.

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