
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 $\alpha$ and $\beta$ are two different planes, and $l$ and $m$ are two different lines, where $l \perp \alpha$, and $m \subset \beta$. Consider the following propositions:  
① If $\alpha \parallel \beta$, then $l \perp m$; ② If $\alpha \perp \beta$, then $l \parallel m$; ③ If $m \parallel \alpha$, then $l \perp \beta$; ④ If $l \perp \beta$, then $m \parallel \alpha$.  
Among these propositions, the correct ones are \_\_\_\_\_\_. (Fill in the serial numbers of all correct propositions).

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