
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 $A=\{x|2<x<9\}$, and set $B=\{x|-2\leq x\leq 5\}$.
(1) Find $A\cap B$; $B\cup (\complement_U A)$;
(2) Given set $C=\{x|a\leq x\leq 2-a\}$, if $C\cup (\complement_U B)=\mathbb{R}$, find the range of the real number $a$.

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