
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, each priced from $0.25$ to $2.50$ in increments of $0.25$. Each time Jane presses the button, the machine randomly selects one of the remaining toys and offers it for sale. Jane will buy the toy if she has enough quarters. The machine only accepts quarters. Jane has 12 quarters and a twenty-dollar bill. What is the probability that Jane has to get change for the twenty-dollar bill before she can buy her favorite toy, which costs $2.25$? Express your answer as a common fraction.

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