
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 one of three shapes - circle, square, or triangle, which is painted in one of three colors - red, blue, or green. Moreover, each color comes in one of four shades - light, medium, dark, or very dark. There are 36 cards, one for every combination of shape, color, and shade. A set of three cards from this deck is called complementary if all the following conditions are met:
i. Each of the three cards has a different shape or all three of the cards have the same shape.
ii. Each of the three cards has a different color or all three cards have the same color.
iii. Each of the three cards has a different shade or all three cards have the same shade.
Determine how many different complementary three-card sets can be formed.

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