<|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
 We want to colour all the squares of an  $ nxn$  board of red or black. The colorations should be such that any subsquare of  $ 2x2$  of the board have exactly two squares of each color. If  $ n\geq 2$   how many such colorations are possible? 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
1
We want to colour all the squares of an  $ nxn$  board of red or black. The colorations should be such that any subsquare of  $ 2x2$  of the board have exactly two squares of each color. If  $ n\geq 2$   how many such colorations are possible?
test