
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 is fair, and the other die is biased so that it comes up five with a probability of $\frac{3}{4}$, while each of the other five sides has an equal probability. Charles randomly chooses one of the two dice and rolls it three times. Given that the first two rolls resulted in fives, calculate the probability that the third roll will also be a five. 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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