
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
Consider the inequality with respect to $x$, $\frac{3}{x} > 1$ ($x \in \mathbb{Z}$). The solution set for this inequality is set $A$. Consider the equation $x^2 - mx + 2 = 0$ ($m \in \mathbb{R}$). The solution set for this equation is set $B$.
(1) Find set $A$.
(2) If $B \cap A = B$, find the range of real numbers $m$.

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