
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 let \\( 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 \\( n \parallel \beta \\).  
\\((4)\\) If \\( m \parallel n \\) and \\( \alpha \parallel \beta \\), then the angle formed by \\( m \\) and \\( \alpha \\) equals the angle formed by \\( n \\) and \\( \beta \\).  
Identify the correct propositions. (Write down all the numbers of the correct propositions)

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