
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
A vending machine contains 10 toys priced between 30 cents and $2.70. The price of each toy is 30 cents higher than the next cheaper one among them. Each press of a button on the machine randomly gives a buyer the chance to purchase one of the remaining toys. John has 10 quarters and a twenty dollar bill to spend, but the machine only accepts quarters. Calculate the probability that John needs to exchange his twenty dollar bill for quarters before he can buy his favorite toy, priced at $\$2.40$. Provide your answer as a simple fraction.

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