
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
Charles has two six-sided dice. One of the dice is fair, and the other die is biased so that it lands on one or six with probability $\frac{1}{3}$ each, and each of the remaining four numbers (2, 3, 4, 5) has a probability of $\frac{1}{15}$. Charles randomly chooses one of the dice and rolls it four times. Given that the first three rolls are a one, find the probability that the fourth roll will be a six. Express your result as $\frac{p}{q}$, where $p$ and $q$ are relatively prime integers. Calculate $p+q$.

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