
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 $f(x)= \sqrt {2- \frac {x+3}{x+1}}$, with its domain defined as $A$, and the function $g(x)=\lg [(x-a-1)(2a-x)]$ (where $a < 1$), with its domain defined as $B$.

1. Find $A$.
2. If $B⊆A$, find the range of possible values for the real number $a$.

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