
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 a universal set $U = \mathbb{R}$, let the set $A = \{x | y = \lg x + \sqrt{2-x}\}$, and the set $B = \{x | \frac{1}{4} < 2^{x-a} \leq 8\}$.
1. When $a=0$, find the intersection of the complement of $A$ in $U$ and $B$;
2. If $A \cup B = B$, determine the range of the real number $a$.

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