
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 the set \( A = \{2,0,1,4\} \),

find the set 
\[ 
B = \{ k \mid k \in \mathbf{R}, k^2 - 2 \in A, k - 2 \notin A \}
\]

and determine the product of all elements in set \( B \).

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