
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 sets $A=\{x|2^{x-6}\leqslant 2^{-2x}\leqslant 1\}$, $B=\{x|x∈A∩N\}$, and $C=\{x|a\leqslant x\leqslant a+1\}$.
(I) Write out all subsets of set $B$;
(II) If $A∩C=C$, find the range of values for the real number $a$.

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