
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 sets $A=\left\{ x\mid (x+4)(x-2) > 0 \right\}$, $B=\left\{ y\mid y=x^{2}-2x+2, x\in \mathbb{R} \right\}$, $C=\left\{ x\mid -4 \leqslant x \leqslant a \right\}$.  
(Ⅰ) Find $A\bigcap B$;  

(Ⅱ) If ${C}_{R}A \subseteq C$, find the range of the real number $a$.

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