
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
Crisp All, a basketball player, is dropping dimes and nickels on a number line. Crisp drops a dime on every positive multiple of 10, and a nickel on every multiple of 5 that is not a multiple of 10. Crisp then starts at 0. Every second, he has a \(\frac{2}{3}\) chance of jumping from his current location \(x\) to \(x+3\), and a \(\frac{1}{3}\) chance of jumping from his current location \(x\) to \(x+7\). When Crisp jumps on either a dime or a nickel, he stops jumping. What is the probability that Crisp stops on a dime?

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