
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
The universal set $U = \mathbb{R}$. Given the sets $A = \{x \mid 3 \leq x < 10\}$ and $B = \{x \mid 1 < x - 1 \leq 6\}$,  
(1) find $A \cap B$ and $A \cup B$;  
(2) if set $C = \{x \mid x > a\}$ satisfies $C \cup A = C$, find the range of values for $a$. (Express the result using intervals or sets)

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