
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 vending machine with 10 toys where prices increase by 50 cents from the least expensive to the most expensive. The range is from 50 cents to $\$5.00$. Each time Mary presses the button, it dispenses a random available toy, and she can buy it if she has enough coins (the machine only accepts coins). Mary starts with 12 quarters and a \$20 bill. Among these toys, there are two of her favorites, each costing $\$4.50$. What is the probability that Mary has to exchange her \$20 bill for quarters at the machine before she can buy either of her favorite toys? Express your answer as a common fraction.

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