
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
Samantha has two six-sided dice. The first die is fair, while the second die is biased such that it lands on three with a probability of $\frac{1}{2}$, and each of the other sides has a probability of $\frac{1}{10}$. Samantha randomly picks one die and rolls it four times. Given that the first three rolls all result in threes, find the probability that the fourth roll will also be a three. Express your answer as a reduced fraction $\frac{p}{q}$ and find $p+q$.

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