
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
Let  $n$  be a natural composite number. For each proper divisor  $d$  of  $n$  we write the number  $d + 1$  on the board.  Determine all natural numbers  $n$  for which the numbers written on the board are all the proper divisors of a natural number  $m$ . (The proper divisors of a natural number  $a> 1$  are the positive divisors of  $a$  different from  $1$  and  $a$ .)

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