
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
A digital music player has 12 songs of varying lengths. When arranged by duration, the shortest song lasts 40 seconds, and each subsequent song is 40 seconds longer than the one before it. The user's favorite song is 5 minutes long. The player shuffles all the songs and plays them in random order without repeating any song. What is the probability that the user listens to the first 6 minutes of music without hearing their favorite song in full? Express your answer as a common fraction.

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