
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
Let set $A$ be the domain of the function $y=\ln (-x^{2}-2x+8)$, and set $B$ be the range of the function $y=x+\dfrac{1}{x}+1$.

   Find: $(1)A\cap B$ and $A\cup B$; 

           $(2)A\cap (C_{R}B)$.

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