
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
Each card in an expanded deck has a picture of one shape - circle, square, or triangle, a color - red, blue, or green, a size - small, medium, or large, and each color is painted in one of three shades - light, medium, or dark. The deck now has 81 cards, each representing every possible combination of shape, color, size, and shade. A set of three cards is called complementary if all the following conditions are met:
i. Each of the three cards has a different shape or all three cards have the same shape.
ii. Each of the three cards has a different color or all three cards have the same color.
iii. Each of the three cards has a different size or all three cards share the same size.
iv. Each of the three cards has a different shade or all three cards feature the same shade.
How many different complementary three-card sets are there in this expanded deck?

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