
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 an enhanced deck has a drawing with four attributes - shape (circle, square, or triangle), color (red, blue, or green), shade (light, medium, or dark), and pattern (striped, solid, or dotted). The deck has 81 cards, with each possible combination of attributes represented exactly once. A set of three cards from this deck is considered complementary if:
i. Each of the three cards has a different shape or all three have the same shape.
ii. Each of the three cards has a different color or all three have the same color.
iii. Each of the three cards has a different shade or all three have the same shade.
iv. Each of the three cards has a different pattern or all three have the same pattern.
Determine how many different complementary three-card sets exist.

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