
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 set A be the domain of the function $y=\lg \frac{1+x}{2-x}$, and set B be the solution set of the inequality $(ax-1)(x+2) \geq 0$ ($a>0$).  
(1) If $a=1$, find $A \cap B$;  
(2) If $B \subseteq \complement_{\mathbb{R}}A$, find the range of the real number $a$.

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