
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 that \\(a\\), \\(b\\), and \\(c\\) are three different lines, and \\(a\\) is parallel to plane \\(\alpha\\), \\(b\\) is parallel to plane \\(\beta\\), with \\(\alpha \cap \beta = c\\). Consider the following propositions:

\\(①\\) If \\(a\\) is not perpendicular to \\(c\\), then \\(a\\) and \\(b\\) must not be perpendicular;

\\(②\\) If \\(a \parallel b\\), then it must be that \\(a \parallel c\\);

\\(③\\) If \\(a \perp b\\) and \\(a \perp c\\), then it must be that \\(\alpha \perp \beta\\).

The correct proposition(s) is/are \_\_\_\_\_\_\_\_.

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