
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 the three colors - red, blue, or green, and one of the three shades - light, medium, or dark. In addition, each card has a pattern of dots, stripes, or solids. The deck now has 81 cards, with every shape-color-shade-pattern combination represented. A set of three cards from the deck is called complementary if:
i. Either each of the three cards has a different shape or all three cards have the same shape.
ii. Either each of the three cards has a different color or all three of the cards have the same color.
iii. Either each of the three cards has a different shade or all three of the cards have the same shade.
iv. Either each of the three cards has a different pattern or all three of the cards have the same pattern.
How many different complementary three-card sets are there?

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