
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 lines $m$ and $l$, and planes $\alpha$ and $\beta$, with $m \perp \alpha$ and $l \subset \beta$. Among the following propositions, the correct ones are:

① If $\alpha \parallel \beta$, then $m \perp l$;  
② If $\alpha \perp \beta$, then $m \parallel l$;  
③ If $m \perp l$, then $\alpha \parallel \beta$;  
④ If $m \parallel l$, then $\alpha \perp \beta$.

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