
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
There is a machine with 10 toys in it that each cost between 50 cents and $2.50, with each toy being 25 cents more expensive than the next most expensive one. Each time Sam presses the big red button on the machine, the machine randomly selects one of the remaining toys and gives Sam the option to buy it. If Sam has enough money, he will buy the toy, the red button will light up again, and he can repeat the process. If Sam has 10 quarters and a twenty dollar bill and the machine only accepts quarters, what is the probability that Sam has to get change for the twenty dollar bill before he can buy his favorite toy- the one that costs $2.25? Express your answer as a common fraction.

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