
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
Each of two boxes contains both red and blue marbles, and the total number of marbles in the two boxes is $20$. One marble is taken out of each box randomly. The probability that both marbles are red is $3/8$, and the probability that both marbles are blue is $p/q$, where $p$ and $q$ are relatively prime positive integers. What is $p + q$?

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