
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
Alice, Bob, Carol, and Dave repeatedly take turns tossing a die in the order Alice, Bob, Carol, Dave, then repeat from Alice, and so on. Find the probability that Carol will be the first one to toss a six. (The probability of obtaining a six on any toss is $\frac{1}{6}$, independent of the outcome of any other toss.)
A) $\frac{125}{671}$
B) $\frac{125}{1296}$
C) $\frac{625}{1296}$
D) $\frac{78125}{1679616}$
E) $\frac{125}{1296}$

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