
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 are 10 toys in a vending machine, each toy costing between 50 cents and $5.00, with each subsequent toy costing 50 cents more than the previous. Each time Sam pushes the big red button, the machine randomly selects one of the remaining toys and offers it to Sam. If Sam has enough coins, he will buy it. The machine only accepts quarters. If Sam has 10 quarters and a twenty-dollar bill, what is the probability that Sam needs to break his twenty-dollar bill to buy his favorite toy, which costs $\$3.00$? Express your answer as a common fraction.

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