
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
Lucy has 10 toys in a vending machine, each costing between 25 cents and 2 dollars, with each toy being 15 cents more expensive than the next most expensive one. Each time she presses the big green button on the machine, it randomly selects one of the remaining toys and offers it to her. Lucy has 10 quarters and a ten-dollar bill, but the machine only accepts quarters. What is the probability that Lucy has to get change for the ten-dollar bill before she can buy her favorite toy, which costs $1.65? Express your answer as a common fraction.

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