
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 MP3 player. The length of each song varies, with the shortest song lasting 30 seconds and each subsequent song being 40 seconds longer than the previous one. Celeste’s favorite song is now 4 minutes, 30 second long. The o-Pod plays the songs in a random sequence before any song is repeated. What is the probability that she hears the first 5 minutes of music—played with no breaks between songs—without hearing every second of her favorite song? Express your answer as a fraction.

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