
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
Every card in a deck features one of three symbols - star, heart, or diamond, each in one of three colors - red, yellow, or blue, and each with one of three textures - smooth, rough, or bumpy. This deck has 27 unique cards, with each possible symbol-color-texture combination represented. A set of three cards from this deck is considered complementary if:
i. Each of the three cards has either a different symbol or the same symbol.
ii. Each of the three cards has either a different color or the same color.
iii. Each of the three cards has either a different texture or the same texture.
Calculate how many different complementary three-card sets are there.

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