
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
Amy, Beth, and Jo listened to five different songs. They discussed which songs they liked under these conditions: No song is liked by all three, and for any two of them, there is at least one song liked by them but disliked by the third. Additionally, no individual likes more than three of the songs. In how many different ways can such preferences be arranged?
A) 1320
B) 1560
C) 1720
D) 1890
E) 2010

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