
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 $l$ and $m$ be two non-coincident lines, and $\alpha$ and $\beta$ be two non-coincident planes. Among the following statements, the correct ones are \_\_\_\_\_\_.
① If $l \parallel \alpha$ and $\alpha \perp \beta$, then $l \perp \beta$;  
② If $l \perp m$, $l \perp \alpha$, and $m \perp \beta$, then $\alpha \perp \beta$;  
③ If $l \perp \alpha$, $\alpha \perp \beta$, and $m \subset \beta$, then $l \parallel m$;  
④ If $l \perp \beta$ and $\alpha \perp \beta$, then $l \parallel \alpha$ or $l \subset \alpha$.

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