
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
Jessica has three six-sided dice: One fair die, a second biased die that comes up six with probability $\frac{1}{2}$ (and the other five sides each with probability $\frac{1}{10}$), and a third biased die that comes up six with probability $\frac{3}{4}$ (and the other five sides each with equal probability). Jessica chooses one of these dice at random and rolls it three times. Given that the first two rolls result in sixes, find the probability that the third roll will also be a six. Express the answer as $\frac{p}{q}$ where $p$ and $q$ are relatively prime.

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