
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 $A$ and $B$ be two non-empty sets. Define: $A\odot B=\{x| x\in A\cup B \text{ and } x\notin A\cap B\}$. Given $A=\{x|y=\sqrt{x-1}\}$, $B=\{x||x-1| > 1\}$, then $A\odot B=\_\_\_\_\_\_$. (Express using intervals)

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