
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 $U=\mathbb{R}$, set $A=\{x|x^2-3x-18\geq0\}$, and $B=\left\{x\middle| \frac{x+5}{x-14}\leq0\right\}$.  
(1) Find $(\complement_{U}B) \cap A$.  
(2) If set $C=\{x|2a<x<a+1\}$, and $B\cap C=C$, find the range of the real number $a$.

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