
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 $f(x)=\log\left(\frac{1+x}{x-2}\right)$ has domain $A$, and the 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 the real number $a$.

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