
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 inequality in terms of \\(x\\), \\({{x}^{2}}-2(m+1)x+4m\geqslant 0\\).

\\((1)\\) If the solution set of the inequality is \\(\mathbb{R}\\), find the value of the real number \\(m\\);

\\((2)\\) Find the solution set of the inequality;

\\((3)\\) If the above inequality holds for any \\(x \in [-1,1]\\), find the range of values for the real number \\(m\\).

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