
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
Define the set operation "\*": $A \times B = \{(x, y) | x \in A, y \in B\}$, called the "Cartesian product" of sets A and B. If $A = \{x | x^2 - 2|x| \leq 0, x \in \mathbb{N}\}$, $B = \{1, 2, 3\}$, then find $(A \times B) \cap (B \times A)$.

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