
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 universal set $U$ ($= \mathbb{R}$), set $A$ ($= \left\{x \mid 3^{x(x-3)} < 1 \right\}$), and set $B$ ($= \left\{x \mid y = \sqrt{\log_{2}(x-1)} \right\}$), find the intersection of set $A$ and set $B$, denoted as $A \cap B$.

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