
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, and Carl take turns rolling a die. Alice rolls first, Bob always rolls after Alice, and Carl always rolls after Bob. What is the probability that Carl is the first to roll a 6, where the probability of rolling a 6 on any single roll is $\frac{1}{6}$, and each roll is independent of the others.

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