
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  $n\geq 4$  be a positive integer.Out of  $n$  people,each of two individuals play table tennis game(every game has a winner).Find the minimum value of  $n$ ,such that for any possible outcome of the game,there always exist an ordered four people group  $(a_{1},a_{2},a_{3},a_{4})$ ,such that the person  $a_{i}$  wins against  $a_{j}$  for any  $1\leq i<j\leq 4$ 

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