
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
Every card in a deck has a picture of one shape (circle, square, or triangle), which is painted in one of three colors (red, blue, or green), and each color is applied in one of three shades (light, medium, or dark). Additionally, each card has one of three sizes (small, medium, large). The deck has 81 cards, with every shape-color-shade-size combination represented. A set of three cards from this deck is called complementary if all of the following statements are true:
i. Either each of the three cards has a different shape or all three have the same shape.
ii. Either each of the three cards has a different color or all three have the same color.
iii. Either each of the three cards has a different shade or all three have the same shade.
iv. Either each of the three cards has a different size or all three have the same size.
How many different complementary three-card sets are there?

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