
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 a line \\(m\\) contained in plane \\(\beta\\), then among the following four propositions:

\\(①\\) If \\(\alpha \parallel \beta \Rightarrow l \perp m\\); \\(②\\) If \\(\alpha \perp \beta \Rightarrow l \parallel m\\);

\\(③\\) If \\(l \parallel m \Rightarrow \alpha \perp \beta\\); \\(④\\) If \\(l \perp m \Rightarrow \alpha \parallel \beta\\);

The correct proposition numbers are \_\_\_\_\_\_\_.

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