
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 the set $A=\{x|x^2-x-2<0\}$, $B=\{x|x(3-x)>0\}$, and $M=\{x|2x-a<0\}$.  
(1) Find $A\cap(\complement_{U}B)$;  
(2) If $(A\cup B) \subseteq M$, find the range of the real number $a$.

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