
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 a sequence of \( n \) terms \( a_1, a_2, \ldots, a_n \) has the following property: For any non-empty subset \( B \) of \( S \), there exist \( |B| \) consecutive elements in the sequence that exactly form the set \( B \). Find the minimum value of \( n \).

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