
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
Celeste has 12 songs stored on her o-Pod, each song differing in length. When ordered by length, the shortest song is 45 seconds long, and each subsequent song is 45 seconds longer than the previous one. Her favorite song is 4 minutes, 30 seconds long. The o-Pod plays all songs in a random order before repeating any song. What is the probability that Celeste hears the first 6 minutes of music - with no pauses between songs - without hearing all of her favorite song? Express your answer as a common fraction.

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