
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 $A=\{y|y=\log_{2}x, x>1\}$, and $B=\{y|y=2^{x}, 0<x<2\}$, the set $C$ is the domain of the function $$f(x)= \sqrt {a+1-x}+\ln(x-a)$$.
(Ⅰ) Find $A\cap B$;
(Ⅱ) If $C\subseteq A\cap B$, find the range of the real number $a$.

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