
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 the universal set be $R$. The solution set of the inequality $\frac{x+3}{x-7}＜0$ is denoted as $A$, and the solution set of the inequality $|x-4|\leqslant 6$ is denoted as $B$.  
$(1)$ Find $A\cap B$;  
$(2)$ Find $\complement _{R}(A\cup B)$.

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