
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 that line $l$ is perpendicular to plane $\alpha$, and line $m$ is contained within plane $\beta$, evaluate the following four statements:  
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 $\alpha \parallel \beta$.  
Identify the correct statement(s) from the above.

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