
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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