
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 $A$ be defined by $A=\{x \mid 1 \leq x < 5\}$, and the set $B$ by $B=\{x \mid 2 < x < 8\}$. Find:
(1) $A \cap B$;
(2) $A \cup B$;
(3) $(C_U A) \cap (C_U B)$.

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