<|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
 The archipelago consists of $N \geq 7$ islands. Any two islands are connected by no more than one bridge. It is known that from each island there are no more than 5 bridges, and among any 7 islands there are definitely two connected by a bridge. What is the maximum possible 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
36
The archipelago consists of $N \geq 7$ islands. Any two islands are connected by no more than one bridge. It is known that from each island there are no more than 5 bridges, and among any 7 islands there are definitely two connected by a bridge. What is the maximum possible value of $N$?
test