
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  $S$  be the set of all natural numbers with the property: the sum of the biggest three divisors of number  $n$ , different from  $n$ , is bigger than  $n$ . Determine the largest natural number  $k$ , which divides any number from  $S$ .
(A natural number is a positive integer)

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