
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
Liam, Noah, and Olivia listen to five different songs and discuss which ones they like. No song is liked by all three. Furthermore, for each of the three pairs of the children, there is at least one song liked by those two children 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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