
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 expanded deck has a picture of one shape (circle, square, triangle), colored in one of three colors (red, blue, green), in one of three shades (light, medium, dark), and sized in three variants (small, medium, large). This deck thus contains 81 unique cards, representing every possible combination. A set of three cards from this deck is called complementary if all the following statements hold:
i. Either each of the three cards has a different shape or all three have the same shape.
ii. Either each of the three cards has a different color or all three share the same color.
iii. Either each of the three cards has a different shade or all have the same shade.
iv. Either each of the three cards has a different size or all three are the same size.
How many different complementary three-card sets are there?

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