
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 line $m$, line $l$, and planes $\alpha$, $\beta$, with $l \perp \alpha$, $m \subset \beta$, the following four propositions are given:  
① If $\alpha \parallel \beta$, then $l \perp m$  
② If $\alpha \perp \beta$, then $l \parallel m$  
③ If $l \parallel m$, then $\alpha \perp \beta$  
④ If $l \perp m$, then $\alpha \parallel \beta$  
Among these, the true propositions are \_\_\_\_\_\_ (Please fill in the numbers of all correct propositions)

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