
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 \\(m\\) and \\(n\\) are two different lines, and \\(α\\) and \\(β\\) are two different planes, there are the following four propositions:

\\(①\\) If \\(α⊥β\\), \\(m⊂α\\), \\(n⊂β\\), then \\(m⊥n\\);

\\(②\\) If \\(m⊥α\\), \\(n⊥β\\), \\(m⊥n\\), then \\(α⊥β\\);

\\(③\\) If \\(m∥α\\), \\(n∥β\\), \\(m∥n\\), then \\(α∥β\\);

\\(④\\) If \\(m⊥α\\), \\(n∥β\\), \\(α∥β\\), then \\(m⊥n\\).

Among these, the correct proposition numbers are \_\_\_\_\_\_\_\_.

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