
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 \\(m\\) and \\(n\\) be two different lines in space, and \\(α\\) and \\(β\\) be two different planes in space. Consider the following propositions:  
\\(①\\) If \\(m \parallel α\\) and \\(m \parallel β\\), then \\(α \parallel β\\);  
\\(②\\) If \\(m \parallel α\\) and \\(m \parallel n\\), then \\(n \parallel α\\);  
\\(③\\) If \\(m \perp α\\) and \\(m \parallel β\\), then \\(α \perp β\\);  
\\(④\\) If \\(m \perp α\\) and \\(α \parallel β\\), then \\(m \perp β\\)  
Write down the numbers of all correct propositions \_\_\_\_\_\_.

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