
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
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?

Present the answer in LaTex format: \boxed{Your answer}
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