
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
Determine all integers  $s \ge 4$  for which there exist positive integers  $a$ ,  $b$ ,  $c$ ,  $d$  such that  $s = a+b+c+d$  and  $s$  divides  $abc+abd+acd+bcd$ .

*Proposed by Ankan Bhattacharya and Michael Ren*

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