
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 displays a shape (circle, square, or triangle), a color (red, blue, or green), a shade (light, medium, or dark), and a pattern (plain, striped, or dotted). There are 81 cards, each representing a unique combination of these four attributes. A set of three cards from this deck is termed complementary if:
i. Either all three cards have different shapes or all have the same shape.
ii. Either all three cards have different colors or all have the same color.
iii. Either all three cards have different shades or all have the same shade.
iv. Either all three cards have different patterns or all have the same pattern.
What are the number of different complementary three-card sets?

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