
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
Given that Amy, Beth, and Jo listen to five different songs, determine the number of ways in which no song is liked by all three and for each of the three pairs of the girls, there is at least one song liked by those two girls but disliked by the third.

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