
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 \\(α\\) and \\(β\\) be two planes, and \\(m\\) and \\(n\\) be two lines. Consider the following four propositions:  
\\(①\\) If \\(m \parallel n\\) and \\(n \subset α\\), then \\(m \parallel α\\);  
\\(②\\) If \\(α \perp β\\), \\(α \cap β = n\\), and \\(m \perp n\\), then \\(m \perp β\\);  
\\(③\\) If \\(m \perp α\\) and \\(n \nparallel α\\), then \\(m \perp n\\);  
\\(④\\) If \\(m \perp n\\), \\(m \perp α\\), and \\(n \nparallel β\\), then \\(α \perp β\\).  
Among these propositions, the correct ones are __________ (Fill in the serial numbers of all correct propositions).

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