
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
On a board, several distinct natural numbers are written. If the smallest number is increased 32 times, the sum of the numbers on the board will become 581. If the largest number is increased 17 times, the sum of the numbers on the board will also become 581. What numbers could be written on the board?

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