
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
Assume a deck of 27 cards where each card features one of three symbols (star, circle, or square), each symbol painted in one of three colors (red, yellow, or blue), and each color applied in one of three intensities (light, medium, or dark). Each symbol-color-intensity combination is unique across the cards. A set of three cards is defined as complementary if:
i. Each card has a different symbol or all have the same symbol.
ii. Each card has a different color or all have the same color.
iii. Each card has a different intensity or all have the same intensity.
Determine the number of different complementary three-card sets available.

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