
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 9 toys, each priced between 50 cents and 4.50 dollars in 50-cent increments. Each time Leo presses the green button on the machine, it randomly selects one of the remaining toys and offers it for sale. If Leo has enough money, he buys the toy, and he can press the button again. If Leo has 10 fifty-cent coins and a twenty-dollar bill, and the machine only accepts fifty-cent coins, what is the probability that Leo needs to get change for the twenty-dollar bill before he can buy his favorite toy, which costs $4.00? Express your answer as a common fraction.

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