
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 is different 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 5 minutes and 15 seconds long. The o-Pod will play all the songs in random order before repeating any song. What is the probability that she hears the first 7 minutes of music (without any pauses between songs) without hearing every second of her favorite song? Express your answer as a common fraction.

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