
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 the following five propositions:  
\\(①\\) The solution set of the inequality \\(x^{2}-4ax+3a^{2} < 0\\) is \\(\{x|a < x < 3a\}\\);  
\\(②\\) If the function \\(y=f(x+1)\\) is an even function, then the graph of \\(y=f(x)\\) is symmetric about \\(x=1\\);  
\\(③\\) If the solution set of the inequality \\(|x-4|+|x-3| < a\\) is empty, then it must be that \\(a \geqslant 1\\);  
\\(④\\) The graph of the function \\(y=f(x)\\) has at most one intersection point with the line \\(x=a\\);  
\\(⑤\\) If angles \\(α\\) and \\(β\\) satisfy \\(\cos α \cdot \cos β = 1\\), then \\(\sin (α+β) = 0\\).  
The correct propositions are \_\_\_\_\_\_.

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