
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 $m, n$ are lines and $\alpha, \beta$ are planes in space, consider the following propositions:  
① If $m \perp \alpha$ and $m \perp n$, then it implies $n \parallel \alpha$;  
② If $m \subseteq \alpha$, $n \subseteq \beta$, and $\alpha \parallel \beta$, then it implies $m \parallel n$;  
③ If $m \perp \alpha$ and $m \perp \beta$, then it implies $\alpha \parallel \beta$;  
④ If $m \perp \beta$ and $n \perp \beta$, then it implies $m \parallel n$.  
Among these propositions, the correct ones are ______.

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