
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 9 toys each costing from 50 cents to 4 dollars, increasing by 50 cents for each toy. Each time Sam presses the big red button on the machine, a toy is randomly selected for him to buy if he can afford it. Sam starts with 10 half-dollar coins and a twenty-dollar bill, and the machine only accepts half-dollar coins. What is the probability that Sam needs to get change for the twenty-dollar bill before he can buy his favorite toy, which costs 3.5 dollars? Express your answer as a common fraction.

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