
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
We call the average magic of a set of numbers the ratio of their sum to their product. Initially, several (more than one) different natural numbers are written on the board. After the smallest of them was erased from the board, the average magic of all the remaining numbers on the board increased threefold. Find what the numbers on the board were.

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