
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
Two boxes contain black and white marbles, with a total of 30 marbles. One marble is taken out of each box randomly. The probability that three marbles drawn (one by one without replacement) from each box are all black is $\frac{18}{25}$. If the probability that all marbles drawn this way from one box are white is represented as $\frac{p}{q}$ where $p$ and $q$ are coprime integers, what is $p + q$?

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