
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
A person has two eight-sided dice. One die is fair, and the other die is biased such that it rolls an eight with a probability of $\frac{3}{4}$, and each of the other seven faces has a probability of $\frac{1}{28}$. The person selects a die at random and rolls it four times. Given that the first three rolls are all eights, calculate the probability that the fourth roll is also an eight.

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