
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 toy costing 25 cents more than the previous one, starting from 50 cents. Each time he presses a button, the machine randomly selects one of the remaining toys to offer him. Sam, who has 10 quarters and a five-dollar bill, will buy the toy if he can afford it using only quarters. The machine only accepts quarters. Determine the probability that Sam must exchange his five-dollar bill for quarters before he can buy his favorite toy, priced at $2.25. Express your probability as a common fraction.

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