
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
Let the domain of the function $f(x) = \frac{1}{\sqrt{2-x}}$ be $A$, and the domain of $g(x) = \log((x-a-1)(2a-x))$ (where $a<1$) be $B$.
(1) Find $A$; (2) If $B \subseteq A$, find the range of the real number $a$.

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