
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, there are 10 natural numbers written, among which there may be equal ones, and the square of each of them divides the sum of all the others. What is the greatest number of different numbers that can be among the written ones?

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