
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 universal set be $U = \mathbb{R}$, set $A = \{x | \frac{x+1}{x-2} < 0\}$, $B = \{x | ax-1 > 0, a > 0\}$. If $B \subset \overline{A}_U$, find the range of real number $a$.

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