
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 positive integers  $n$  for which there exist positive integers  $a, b,$  and  $c$  that satisfy the following three conditions: $\bullet$   $a+b+c=n$  $\bullet$   $a$  is a divisor of  $b$  and  $b$  is a divisor of  $c$  $\bullet$   $a < b < c$ 

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