
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 $A=\left\{{x||x-\frac{1}{2}|＜1}\right\}$, $B=\left\{{x|\frac{1}{x}≥1}\right\}$, and $A\times B=\{x\left|\right.x\in A\cup B$ and $x\notin A\cap B\}$, determine the set $A\times B$.

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