
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}\\), let the set \\(A=\{x|x < -4 \text{ or } x > 1\}\\), \\(B=\{x|-3\leqslant x-1\leqslant 2\}\\),  
\\((1)\\) find \\(A\cap B\\) and \\((\complement_{U}A)\cup(\complement_{U}B)\\);  
\\((2)\\) if the set \\(M=\{x|2k-1\leqslant x\leqslant 2k+1\}\\) is a subset of set \\(A\\), find the range of the real number \\(k\\).

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