
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 a deck features a shape (circle, square, triangle), a color (red, blue, green), a shade (light, medium, dark), and a pattern (striped, dotted, plain). The deck comprises 81 cards, with each possible combination of shape, color, shade, and pattern represented once. A set of three cards is termed complementary if:
i. Each of the three cards has a different shape or all have the same shape.
ii. Each of the three cards has a different color or all have the same color.
iii. Each of the three cards has a different shade or all have the same shade.
iv. Each of the three cards has a different pattern or all 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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