
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 $m$ and $n$ are two non-coincident lines, and $\alpha$ and $\beta$ are two non-coincident planes, consider the following propositions:  
① If $m \subset \beta$ and $\alpha \parallel \beta$, then $m \parallel \alpha$;  
② If $m \parallel \beta$ and $\alpha \parallel \beta$, then $m \parallel \alpha$;  
③ If $m \perp \alpha$, $\beta \perp \alpha$, and $m \parallel n$, then $n \parallel \beta$;  
④ If $m \perp \alpha$, $n \perp \beta$, and $\alpha \parallel \beta$, then $m \parallel n$.  
Identify all correct conclusions from the above. (Please fill in the sequence numbers of all correct conclusions.)

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