
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 such that it rolls a six with probability \( \frac{3}{4} \) and each of the other five sides with probability \( \frac{1}{20} \). Charles randomly selects one of the two dice and rolls it four times. Given that the first three rolls are sixes, find the probability that the fourth roll will also be a six. Express your answer as \( \frac{p}{q} \), where \( p \) and \( q \) are relatively prime positive integers, and find \( p+q \).

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