
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|1\leqslant x < 6\}\\), \\(B=\{x|0\leqslant \log_{2}(x-1) < 3\}\\).  
\\((1)\\) Find \\(A\cap B\\), \\((\complement_{U}B)\cup A\\)  
\\((2)\\) Given \\(C=\{x|2a-1 < x < a+1\}\\), if \\(C\cap B=C\\), find the range of the real number \\(a\\).

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