
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 \( A \) be any set of 7 real numbers. Define the set \( B = \{xy \mid x, y \in A \text{ and } x \neq y\} \). If \( |B| \) denotes the number of elements in the set \( B \), what is \( |B|_{\text{max}} + |B|_{\text{min}} \)?

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