
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 $A=\{x\mid 2 < x < 9\}$, and set $B=\{x\mid -2 \leqslant x \leqslant 5\}$.

1. Find $A \cap B$ and $B \cup (\lnot_{U}A)$.
2. Given set $C=\{x\mid a \leqslant x \leqslant 2-a\}$, if $C \cup (\lnot_{U}B)=\mathbb{R}$, find the range of values for the real number $a$.

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