
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 $A=\{x|-1<x<1\}$, $B=\{x|2\leq4^x\leq8\}$, $C=\{x|a-4<x\leq2a-7\}$.  
(1) Find $(\complement_U A) \cap B$;  
(2) If $A \cap C = C$, find the range of the real number $a$.

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