
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 \( S = \{1, 2, 3, 4\} \), and consider a sequence \( a_1, a_2, \cdots, a_n \) of \( n \) terms where \( a_i \in S \) such that for any non-empty subset \( B \) of \( S \), there exists a subsequence of \( n \) adjacent terms that forms the set \( B \). Find the minimum value of \( n \).

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