<|im_start|>system
You are a helpful assistant. You first think about the reasoning process in the mind and then provide the user with the answer. You should try to truely solve the question by yourself without cheating.  <|im_end|>
<|im_start|>user
 In an international meeting of  $n \geq 3$  participants, 14 languages are spoken. We know that:

- Any 3 participants speak a common language.

- No language is spoken more that by the half of the participants.

What is the least value of  $n$ ? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>
<|im_start|>assistant
Let me solve this step by step.
<think>
user
8
In an international meeting of  $n \geq 3$  participants, 14 languages are spoken. We know that:

- Any 3 participants speak a common language.

- No language is spoken more that by the half of the participants.

What is the least value of  $n$ ?
test