
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}\\), and the sets \\(A=\{x|1\leqslant x < 5\}\\), \\(B=\{x|2 < x < 8\}\\).
\\((1)\\) Find \\(A\cup B\\) and \\((\complement_{U}A)\cap B\\);
\\((2)\\) If \\(C=\{x|a < x\leqslant a+3\}\\) and \\(C\cap A=C\\), find the range of values for \\(a\\).

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