
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 sets $A=\left\{{x|{\frac{{x-2}}{{x+1}}＜0}}\right\}$ and $B=\{x\left|\right.k \lt x \lt 2-k\}$.<br/>$(1)$ When $k=-1$, find $A\cup B$;<br/>$(2)$ If $A\cap B=B$, find the range of real number $k$.

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