
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
A divisor of a natural number is called a proper divisor if it is greater than 1 and less than the number itself. A natural number is called elegant if it has at least two proper divisors and is divisible by the difference of any two of its proper divisors. Find all elegant numbers.

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