
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 and discuss which ones they like, with no song liked by all three and for each of the three pairs of the girls, there are at least two songs liked by those two girls but disliked by the third, determine the number of different ways this is possible.

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