
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 cube is rotated around its longest axis (i.e., around a line connecting opposite vertices), and black yarn is wound around it tightly without gaps. The yarn will only cover half of the cube (why?). The same can be done with the other three axes, each time using a different color of yarn (black, red, blue, and yellow). This will cover the entire model in different colors, and mixed colors will arise from their combination (the model cube is white and this color is not counted). How many color shades will appear on the cube, and what are they?

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