
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 depicts one shape - circle, square, or triangle - painted in one of three colors - red, blue, or green, in one of three shades - light, medium, or dark, and in one of three sizes - small, medium, or large. This creates a deck of 81 cards, each uniquely combining these four attributes. A set of three cards from the deck is termed complementary if all of the following statements are true for each attribute (shape, color, shade, size):
i. Either each of the three cards has a different value for the attribute or all three cards have the same value for the attribute.
How many different complementary three-card sets are there?

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