
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 universal set \\(U=\mathbb{R}\\), the domain of the function \\(y= \sqrt{x-2} + \sqrt{x+1}\\) is \\(A\\), and the domain of the function \\(y= \frac{\sqrt{2x+4}}{x-3}\\) is \\(B\\).  
\\((1)\\) Find the sets \\(A\\) and \\(B\\).  
\\((2)\\) Find \\((\complement_{U}A) \cup (\complement_{U}B)\\).

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