
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 two distinct lines $l$ and $m$, and two distinct planes $\alpha$ and $\beta$, select the correct statement(s) from the following. (Fill in the sequence number)  
① If $l \perp \alpha$, $m \parallel \beta$, and $\alpha \perp \beta$, then $l \perp m$;  
② If $l \parallel m$, $m \perp \alpha$, and $l \perp \beta$, then $\alpha \parallel \beta$;  
③ If $l \parallel \alpha$, $m \parallel \beta$, and $\alpha \parallel \beta$, then $l \parallel m$;  
④ If $\alpha \perp \beta$, $\alpha \cap \beta = m$, $l \subseteq \beta$, and $l \perp m$, then $l \perp \alpha$.

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