
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 $5.00, with each toy costing 50 cents more than the next most expensive one. Each time Tim presses the big green button on the machine, the machine randomly selects one of the remaining toys and gives Tim the option to buy it. If Tim has enough money, he will buy the toy, the green button will light up again, and he can repeat the process. If Tim has 12 quarters and a twenty-dollar bill and the machine only accepts quarters, what is the probability that Tim has to get change for the twenty-dollar bill before he can buy his favorite toy- the one that costs $4.00? Express your answer as a common fraction.

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