
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 \\(\alpha\\), \\(\beta\\), and \\(\gamma\\) are three planes, and \\(m\\) and \\(n\\) are two lines, there are the following four propositions:  
\\(①\\) If \\(m \perp \alpha\\) and \\(m \subset \beta\\), then \\(\alpha \perp \beta\\);  
\\(②\\) If \\(m \perp n\\) and \\(m \perp \alpha\\), then \\(n \parallel \alpha\\);  
\\(③\\) If \\(\alpha \perp \beta\\) and \\(m \parallel \alpha\\), then \\(m \perp \beta\\);  
\\(④\\) If \\(\alpha \parallel \beta\\), \\(\alpha \cap \gamma = m\\), and \\(\beta \cap \gamma = n\\), then \\(m \parallel n\\).  
Among these propositions, the correct ones are __________. (Write down all the correct proposition numbers.)

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