
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 $A=\{y \mid y=\ln(x+1), x>0\}$, and $B=\{x \mid \frac{1}{2} \leq 2^{x} \leq 8\}$.
(1) Find $(\complement_U A) \cup B$;
(2) Let $C=\{x \mid a-1 \leq x \leq 2a\}$. If $A \cap C = \emptyset$, determine the range of values for the real number $a$.

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