
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
A toy factory produces cubic building blocks of the same size, with each of the six faces painted in one of three colors: red, yellow, and blue, with each color appearing on two faces. If two blocks can be rotated to match the position of each color on the faces, they are considered the same type of block. What is the maximum number of different types of blocks that can be painted?

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