
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 four shapes - circle, square, triangle, or hexagon, each painted in one of three colors - red, blue, or green. Furthermore, each color is rendered in one of three shades - light, medium, or dark. The deck has 36 cards, with every combination of shape, color, and shade represented exactly once. Determine how many different complementary three-card sets can be formed, where a set is defined as 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.

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