
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
All proper divisors of a composite natural number \( n \) are written on a board, each increased by 1. Find all such numbers \( n \) for which the numbers on the board are all the proper divisors of some natural number \( m \). (Proper divisors of a natural number \( a > 1 \) are all of its natural divisors, except for \( a \) and 1.)

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