
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 inequality $x^{2}-(2a+1)x+a(a+1)\leqslant 0$ with the solution set $A$ and the set $B=(-2,2)$.<br/>$(1)$ If $a=2$, find $A\cup B$;<br/>$(2)$ If $A\cap B=\varnothing$, find the range of real number $a$.

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