
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 sets $A=\{x \mid 3 \leq x < 6\}$, and $B=\{x \mid 2 < x < 9\}$.
(1) Find $A \cap B$ and $A \cup B$;
(2) Let $C=\{x \mid a < x < a+1\}$, if $C \subseteq B$, find the range of the real number $a$.

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