
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 \( S = \{1, 2, 3, 4\} \). A sequence of \( n \) terms \( a_1, a_2, \cdots, a_n \) has the following property: for any non-empty subset \( B \) of \( S \) (denote the number of elements in \( B \) as \( |B| \)), there exist \( |B| \) adjacent terms in the sequence that exactly form the subset \( B \). Find the minimum value of \( n \).

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