
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 new card deck is designed with each card displaying one of four shapes (circle, square, triangle, or star), colored in one of the four colors (red, blue, green, or yellow), and each color is represented in one of four shades (light, medium, dark, or very dark). The deck has 64 cards, with each shape-color-shade combination represented uniquely. A set of four cards from the deck is defined as complementary if and only if:
i. Either each of the four cards has a different shape or all four cards have the same shape.
ii. Each of the four cards either has a different color or all four cards have the same color.
iii. Each of the four cards either has a different shade or all four cards have the same shade.

How many different complementary four-card sets are there?

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