
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 that the solution set of the inequality $x^{2}-\left(a+1\right)x+a \lt 0$ is $M$.

(Ⅰ) If $2\in M$, find the range of real numbers for $a$;
(Ⅱ) When $M$ is an empty set, find the solution set of the inequality $\dfrac{1}{x-a} \lt 2$.

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