
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 $U=\mathbb{R}$, $A=\{x|2x-4\geq0\}$, $B=\{x|2\leq2^{x}<16\}$, $C=\{0,1,2\}$.  
(1) Find $C_{\cup}(A\cap B)$;  
(2) If the set $M=(A\cup B)\cap C$, list all proper subsets of $M$.

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