
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
Three friends, Chris, David, and Emily listen to five different tracks and discuss their preferences.  For each two-person combination among the friends, there exists at least one track liked by only those two friends and not by the third.  Calculate the number of different ways this liking pattern can be established among the friends.

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