
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 propositions:  
\\(①\\) The function \\(y=\cos\left(\frac{2}{3}x+\frac{\pi}{2}\right)\\) is an odd function;  
\\(②\\) There exists a real number \\(x\\) such that \\(\sin x+\cos x=2\\);  
\\(③\\) If \\(\alpha\\) and \\(\beta\\) are angles in the first quadrant and \\(\alpha < \beta\\), then \\(\tan \alpha < \tan \beta\\);  
\\(④\\) \\(x= \frac{\pi}{8}\\) is a line of symmetry for the function \\(y=\sin(2x+\frac{5\pi}{4})\\);  
\\(⑤\\) The graph of the function \\(y=\sin(2x+\frac{\pi}{3})\\) is centrally symmetric about the point \\(\left(\frac{\pi}{12},0\right)\\).  
Among these, the correct propositions are \_\_\_\_\_\_.

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