
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 universal set $U=\mathbb{R}$, let set $A=\{x|2^{x-1}\leq 1\}$, and $B=\{x|y=\log_{2}(3-x)\}$.
- (I) Find the set $\complement_U A \cap B$;
- (II) Let set $C=\{x|x<a\}$. If $A \cup C = A$, find the range of the real number $a$.

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