
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 die is fair, and the other die is biased such that it rolls six with a probability of $\frac{3}{4}$ and each of the other five sides with a probability of $\frac{1}{20}$. Charles chooses one of the dice at random and rolls it four times. Given that the first three rolls are sixes, find the probability that the fourth roll is also a six, expressed in simplest form as $\frac{p}{q}$. Calculate $p+q$.

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