
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 \\(a > 0\\), \\(b > 0\\), and \\(4a+b=ab\\),  
\\((\\)I\\()\\) find the minimum value of \\(a+b\\);  
\\((\\)II\\()\\) when \\(a+b\\) reaches its minimum value, the inequality \\(|x-a|+|x-b| \geqslant t^2-2t\\) holds for any \\(x \in \mathbb{R}\\), find the range of \\(t\\).

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