
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 of different lengths. The songs are ordered by length, the shortest being 45 seconds and each subsequent song being 45 seconds longer than the previous one. Her favorite song is 4 minutes and 30 seconds long. The o-Pod will play all the songs in random order without repeating any song. What is the probability that she hears the first 6 minutes of music - there are no 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}
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