
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
Among the following propositions:  
\\(①\\) If \\(ac^{2} > bc^{2}\\), then \\(a > b\\);  
\\(②\\) If \\(\sin \alpha = \sin \beta\\), then \\(\alpha = \beta\\);  
\\(③\\) "The real number \\(a=0\\)" is the necessary and sufficient condition for "the line \\(x-2ay=1\\) and the line \\(2x-2ay=1\\) to be parallel";  
\\(④\\) If \\(f(x)=\log_{2}x\\), then \\(f(|x|)\\) is an even function.  
The correct proposition numbers are \_\_\_\_\_\_.

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