
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
Seth has nine stones: three painted blue, three painted red, and three painted yellow. The blue stones are labeled 1, 2, and 3, as are the red stones and the yellow stones. He builds a vertical tower with three stones, putting one on top of another.

Three stones form a set if any of the following holds:
(i) They all have the same color;
(ii) They are all labeled with the same number;
(iii) They all have different colors;
(iv) They are all labeled with different numbers.

In how many ways can he build a tower that avoids creating a set?

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