
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 $U=\mathbb{R}$, set $A={x\mid 1 < x\leqslant 8}$, $B={x\mid 2 < x < 9}$, and $C={x\mid x\geqslant a}$.

1. Find $A\cap B$ and $A\cup B$;
2. If $A\cap C\neq \varnothing$, find the range of values for $a$.

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