
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 solution set of the quadratic inequality in \\(x\\), \\(a{{x}^{2}}-(a+1)x+b < 0\\), is \\(\left\{x|x < - \dfrac{1}{2} \text{ or } x > 1\right\} \\).

(Ⅰ) Find the values of \\(a\\) and \\(b\\);

(Ⅱ) If the inequality \\(b{{x}^{2}}+(m+2a)x+3-m\geqslant 0\\) holds for any real number \\(m \in [0,4]\\), find the range of the real number \\(x\\).

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