
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
Each girl dislikes at least one song, and for each pair of the girls, there must be at least one song liked by those two but disliked by the third. In how many different ways can this be possible?

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