
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 as $R$, set $A=\{x|y=\lg x+ \sqrt {2-x}\}$, $B=\{x| \frac {1}{4} < 2^{x-a}\leqslant 8\}$.
(1) When $a=0$, find $(∁_{R}A)∩B$;
(2) If $A∪B=B$, find the range of the real number $a$.

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