<|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
 There are $n$ identical-looking balls, one of which is lighter than the others (all other balls have the same weight). Using a balance scale without weights, and needing at least 5 weighings to identify the lighter ball, what is the maximum 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
243
There are $n$ identical-looking balls, one of which is lighter than the others (all other balls have the same weight). Using a balance scale without weights, and needing at least 5 weighings to identify the lighter ball, what is the maximum value of $n$?
test