
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 A = \{x | 3 \leq x \leq 7\}, B = \{x | 2 < x < 10\}, and C = \{x | a < x < a+2\}  
(1) Find A \cup B and A \cap B;  
(2) If C \subseteq (A \cup B), find the range of values for a.

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