
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 non-empty sets, and define $A \times B = \{x | x \in A \cup B \text{ and } x \notin A \cap B\}$. Given $A = \{x | y = \sqrt{2x - x^2}\}$ and $B = \{y | y = 2^x, x > 0\}$, find $A \times B$.

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