
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 $l$ and $m$ are two different lines, and $\alpha$ and $\beta$ are two different planes. The following statements are given:  
① If $l \parallel m$ and $m \subset \alpha$, then $l \parallel \alpha$;  
② If $l \perp \alpha$ and $l \parallel m$, then $m \perp \alpha$;  
③ If $\alpha \perp \beta$, $l \perp \alpha$ and $l \nsubseteq \beta$, then $l \parallel \beta$;  
④ If $\alpha \parallel \beta$, $l \subset \alpha$, and $m \subset \beta$, then $l \parallel m$.  
Among these statements, the correct ones are (Please write down the numbers of all statements you think are correct).

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