
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 sets $A=\{x|(\frac{1}{2})^{x^2-5x+6} \geq \frac{1}{4}\}$, $B=\{x|\log_{2}\frac{x-3}{x-1} < 1\}$, $C=\{x|a-1 < x < a\}$.
(Ⅰ) Find $A \cap B$, $(\mathbb{R} \setminus B) \cup A$;
(Ⅱ) If $C \subseteq A$, find the range of the real number $a$.

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