
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
In a vending machine containing 10 unique toys, the prices range from 25 cents to $2.25, with each successive toy increasing in cost by 25 cents from the one before it. When Peter activates the machine via a button, a toy is randomly offered to him. If Peter has enough coins, he buys it; otherwise, he must break a larger bill. Initially, Peter carries 10 quarters and a $20 bill, but the machine only accepts quarters. Determine the probability that Peter will need to convert the $20 bill into quarters before he can purchase his most desired toy priced at $2.00.

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