
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 propositions:  
\\(①\\) A symmetry axis of the function \\(y=2\sin(2x- \frac{\pi}{3})\\) is \\(x= \frac{5\pi}{12}\\);  
\\(②\\) The graph of the function \\(y=\tan x\\) is symmetric about the point \\((\frac{\pi}{2},0)\\);  
\\(③\\) The sine function is increasing in the first quadrant;  
\\(④\\) If \\(\sin(2x_{1}- \frac{\pi}{4})=\sin(2x_{2}- \frac{\pi}{4})\\), then \\(x_{1}-x_{2}=k\pi\\), where \\(k\in\mathbb{Z}\\).  
Among these four propositions, the correct ones are \_\_\_\_\_\_ (fill in the serial numbers of the correct propositions).

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