
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
Let's modify the original problem slightly. Now, the biased die comes up six with probability $\frac{3}{4}$ and each of the other five sides with probability $\frac{1}{20}$. Charles chooses one of the two dice at random 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.

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