
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 that the universal set is the set of real numbers $\mathbb{R}$, $A=\\left\\{ x\\left| \\dfrac{1-2x}{x-3}\\geqslant 0 \\right. \\right\\}$, and $B=\\left\\{ x\\left| {{x}^{2}}+a\\leqslant 0 \\right. \\right\\}$.

(1) Find $A\\cup B$ when $a=-4$;

(2) Find the range of real number values for $a$ if $\\left( {{C}\_{R}}A \\right)\\cap B=B$.

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