
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
In a vending machine, there are 10 toys that each cost between 50 cents and $4.50 in increments of 50 cents. Sam decides to buy his favorite toy, which costs $4. Each time Sam presses a button on the machine, a randomly selected toy is offered to him for purchase. Sam begins with 12 quarters and a $20 bill. The machine only accepts quarters. What is the probability that Sam must exchange his $20 bill for quarters before he can purchase his favorite toy? Express your answer as a common fraction.

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