
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 function $f(x)=\lg \frac{1+x}{x-2}$ with domain $A$, and set $B$ is the solution set of the inequality ${x}^{2}-(2a+1)x+{a}^{2}+a > 0$.

(I) Find $A$ and $B$;
(II) If $A\cup B=B$, find the range of real number $a$.

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