
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 $U=\mathbb{R}$, let the set $A=\{x \mid 2 < x < 9\}$ and $B=\{x \mid -2 \leq x \leq 5\}$.
1. Find $A \cap B$ and $B \cup (A^c)$, where $A^c$ is the complement of $A$ with respect to $U$.
2. Given the set $C=\{x \mid a \leq x \leq a+2\}$, if $C \subseteq B^c$, find the range of the real number $a$.

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