
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 distinct planes, and \\(m\\) and \\(n\\) be two different lines. Consider the following four propositions:

\\(①\\) If \\(m \perp n\\) and \\(m \perp \alpha\\), then \\(n \parallel \alpha;\\)

\\(②\\) If \\(n \subset \alpha\\), \\(m \subset \beta\\), and \\(\alpha\\) intersects \\(\beta\\) but is not perpendicular, then \\(n\\) and \\(m\\) are not perpendicular;

\\(③\\) If \\(\alpha \perp \beta\\), \\(\alpha \cap \beta = m\\), \\(n \subset \alpha\\), and \\(n \perp m\\), then \\(n \perp \beta;\\)

\\(④\\) If \\(m \parallel n\\), \\(n \perp \alpha\\), and \\(\alpha \parallel \beta\\), then \\(m \perp \beta\\).

Among these propositions, the correct ones are \_\_\_\_ (Fill in the serial numbers).

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