
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 sets $A=\{x \mid 1 \leq x < 7\}, B=\{x \mid 2 < x < 10\},$ and $C=\{x \mid x < a\},$ with the universal set $U=\mathbb{R}.$  
(1) Find $A \cup B$ and $(\overline{A}) \cap B$ where $\overline{A}$ is the complement of A in $\mathbb{R}.$  
(2) If $A \cap C \neq \emptyset,$ find the range of values for $a.$

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