
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
Let $U=\mathbb{R}$, $A=\{x|1\leq x \leq 3\}$, $B=\{x|2 < x < 4\}$, $C=\{x|a \leq x \leq a+1\}$, where $a$ is a real number.  
(1) Find $A \cap B$ and $A \cup (\complement_U B)$.  
(2) If $B \cap C = C$, find the range of values for $a$.

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