
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
For four distinct integers, all pairwise sums and pairwise products were calculated. The obtained sums and products were written on the board. What is the smallest number of distinct numbers that could be on the board?

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