
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
Let the domain of the function $f(x) = \log_2(2x-3)$ be the set $M$, and the domain of the function $g(x) = \frac{1}{\sqrt{(x-3)(x-1)}}$ be the set $N$. Find:  
(Ⅰ) The sets $M$ and $N$;  
(Ⅱ) The intersection of sets $M$ and $N$, and the complement of the union of $M$ and $N$ in $\mathbb{R}$.

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