
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 set $A=\{x | 1 < 2x - 1 < 5\}$, and set $B=\{y | y = (\frac{1}{2})^x, x \geq -2\}$.
(1) Find the intersection of the complement of $A$ in $U$ with $B$.
(2) If set $C=\{x | a - 1 < x - a < 1\}$ and $C \subseteq A$, determine the range of values for the real number $a$.

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