
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
Estella has 12 songs stored on her u-Tunes device. Each song has a unique length. When sorted by length, the durations increase such that the shortest song is 45 seconds long and each subsequent song is 15 seconds longer than its predecessor. Estella’s favorite song is 3 minutes and 45 seconds long. The u-Tunes device shuffles and plays all the songs in a random order before repeating any song. What is the probability that Estella listens to the first 5 minutes of music—without interruptions—without hearing her favorite song in its entirety? Express your answer as a common fraction.

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