<|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
 It is well known that 777-headed dragons have either 9-headed or 13-headed necks. Two dragons are identical if they have the same number of 9-headed necks. How many different 777-headed dragons are there? 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
7
It is well known that 777-headed dragons have either 9-headed or 13-headed necks. Two dragons are identical if they have the same number of 9-headed necks. How many different 777-headed dragons are there?
test