
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 a line $l$ perpendicular to plane $\alpha$, and line $m$ is contained in plane $\beta$, then among the following four propositions: 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 $\alpha \parallel \beta$  
The correct propositions are.

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