<|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
 Using 2 unit squares (unit squares), we can form a 2-tile shape, commonly known as a domino. Clearly, after translations, rotations, and symmetric transformations, dominoes that overlap should be considered the same. Therefore, there is only one type of domino.

Similarly, there are only 2 different types of shapes that can be formed using 3 unit squares.

There are 5 different types of shapes that can be formed using 4 unit squares.

How many different types of shapes can be formed using 5 unit 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
12
Using 2 unit squares (unit squares), we can form a 2-tile shape, commonly known as a domino. Clearly, after translations, rotations, and symmetric transformations, dominoes that overlap should be considered the same. Therefore, there is only one type of domino.

Similarly, there are only 2 different types of shapes that can be formed using 3 unit squares.

There are 5 different types of shapes that can be formed using 4 unit squares.

How many different types of shapes can be formed using 5 unit squares?
test