
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 $\alpha$ and $\beta$ be two non-coincident planes, and $l$, $m$, $n$ be three mutually non-coincident lines. Consider the following four propositions:  
① If $\alpha \parallel \beta$ and $l \subset \alpha$, then $l \parallel \beta$;  
② If $m \subset \alpha$, $n \subset \alpha$, $m \parallel \beta$, $n \parallel \beta$, then $\alpha \parallel \beta$;  
③ If $l \parallel \alpha$ and $l \perp \beta$, then $\alpha \perp \beta$;  
④ If $m$ and $n$ are skew lines, $m \parallel \alpha$, $n \parallel \alpha$, and $l \perp m$, $l \perp n$, then $l \perp \alpha$.  
The correct propositions are numbered as follows:

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