
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
Maria has two six-sided dice. One of the dice is fair, and the other die is biased such that it comes up three with a probability of $\frac{1}{2}$, and each of the other five sides has a probability of $\frac{1}{10}$. Maria chooses one of the two dice at random and rolls it four times. Given that the first three rolls are all threes, the probability that the fourth roll will also be a three is $\frac{p}{q}$, where $p$ and $q$ are relatively prime positive integers. Find $p+q$.

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