
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 function $y= \sqrt{x+1}$ have a domain of set $A$, and the solution set of the inequality ${\log }_{2}(x-1)\leqslant 1$ be set $B$.

$(1)$ Find the sets $A$, $B$;

$(2)$ Find the set $A\cap(C_{R}B)$.

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