
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
Let $l$, $m$, $n$ be three different lines in space, and $\alpha$, $\beta$ be two non-coincident planes in space. The following four propositions are given:  
① If $l$ and $m$ are skew lines, and $m \parallel n$, then $l$ and $n$ are skew lines;  
② If $l \parallel \alpha$, and $\alpha \parallel \beta$, then $l \parallel \beta$;  
③ If $\alpha \perp \beta$, $l \perp \alpha$, and $m \perp \beta$, then $l \perp m$;  
④ If $m \parallel \alpha$, and $m \parallel n$, then $n \parallel \alpha$.  
Among these propositions, the correct ones are. (Please fill in the numbers of all propositions you think are correct)

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