
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
Find all collections of  $63$  integer numbers such that the square of each number is equal to the sum of all other numbers, and not all the numbers are equal. (O. Rudenko)

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