
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 function $f(x) = 2^x$, where $x \in (0, 2)$, its range is denoted as $A$. The function $g(x) = \log_2(x - 2a) + \sqrt{a + 1 - x}$ (where $a < 1$) has its domain denoted as $B$.
(Ⅰ) Find the sets $A$ and $B$;
(Ⅱ) If $B \subseteq A$, find the range of the real number $a$.

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