
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, Dave, and Carol take turns tossing a die. The order is always Alice, then Bob, then Dave, and finally Carol, and this sequence repeats indefinitely. Determine the probability that Carol will be the first among them to toss a six. (Assume the probability of rolling a six on any single toss remains $\frac{1}{6}$.)
A) $\frac{125}{671}$
B) $\frac{125}{1296}$
C) $\frac{625}{1296}$
D) $\frac{25}{91}$
E) $\frac{5}{18}$

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