<|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
 Each of the squares of an  $8 \times 8$  board can be colored white or black. Find the number of colorings of the board such that every  $2 \times 2$  square contains exactly 2 black squares and 2 white squares. 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
8448
Each of the squares of an  $8 \times 8$  board can be colored white or black. Find the number of colorings of the board such that every  $2 \times 2$  square contains exactly 2 black squares and 2 white squares.
test