
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 set $A=\{x|2^{x-6} \leq 2^{-2x} \leq 1\}$, $B=\{x|x \in A \cap \mathbb{N}\}$, $C=\{x|a \leq x \leq a+1\}$.
(Ⅰ) List all subsets of set B;
(Ⅱ) If $A \cap C = C$, find the range of the real number $a$.

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