
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
A deck now consists of cards with four different shapes (circle, square, triangle, star), each painted in one of four colors (red, blue, green, yellow) and in one of four shades (light, medium, dark, very dark). The deck contains 64 cards, each combination of shape-color-shade is unique. A set of three cards is called 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.
Determine how many different complementary three-card sets can be formed.

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