
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
Sam encounters a vending machine with 10 toys each varying in price from 50 cents to $2.50, increasing by 25 cents for each toy. Sam's favorite toy now costs $2.25. Initially, Sam has 12 quarters and a twenty-dollar bill with the machine only accepting quarters. What is the probability that Sam has to break his twenty-dollar bill to buy his favorite toy if he can only use the quarters initially? Provide your answer as a simplified fraction.

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