
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 \( n \) (where \( n > 3 \)) be a given integer. Find the largest integer \( d \) such that, for any set \( S \) consisting of \( n \) integers, there exist four distinct non-empty subsets (which may have non-empty intersections) such that the sum of the elements in each subset is divisible by \( d \).

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