
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
Let \\(\alpha\\) and \\(\beta\\) be two planes, and \\(m\\) and \\(n\\) be two lines. Consider the following four propositions:  
\\(①\\) If \\(m \perp n\\), \\(m \perp \alpha\\), and \\(n \parallel \beta\\), then \\(\alpha \perp \beta\\).  
\\(②\\) If \\(m \perp \alpha\\) and \\(n \parallel \alpha\\), then \\(m \perp n\\).  
\\(③\\) If \\(\alpha \parallel \beta\\) and \\(m \subset \alpha\\), then \\(m \parallel \beta\\).  
\\(④\\) If \\(m \parallel n\\) and \\(\alpha \parallel \beta\\), then the angle formed by \\(m\\) with \\(\alpha\\) is equal to the angle formed by \\(n\\) with \\(\beta\\).  
Among these propositions, the correct ones are \_\_\_\_\_\_ (fill in the numbers).

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