
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 four conclusions:  
\\((1)\\) The center of symmetry of the function \\(f(x)= \dfrac {x-1}{2x+1}\\) is \\((- \dfrac {1}{2},- \dfrac {1}{2})\\);  
\\((2)\\) If the equation in \\(x\\), \\(x- \dfrac {1}{x}+k=0\\), has no real roots for \\(x \in (0,1)\\), then the range of \\(k\\) is \\(k \geqslant 2\\);  
\\((3)\\) Given that point \\(P(a,b)\\) and point \\(Q(1,0)\\) are on opposite sides of the line \\(2x-3y+1=0\\), then \\(3b-2a > 1\\);  
\\((4)\\) If the graph of the function \\(f(x)=\sin (2x- \dfrac {\pi}{3})\\) is shifted to the right by \\(\varphi (\varphi > 0)\\) units and becomes an even function, then the minimum value of \\(\varphi\\) is \\( \dfrac {\pi}{12}\\),  
among these conclusions, the correct ones are: \_\_\_\_\_\_ .

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