
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
1. Solve the inequality about $x$: $\frac{x+3}{x+1} \leqslant 2$;
2. Denote the solution set of the inequality in 1. as $A$, and the function $g(x)=\lg [(x-a-1)(2a-x)]$, $(a < 1)$'s domain as $B$. If $B \subseteq A$, find the range of the real number $a$.

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