
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
Michael has a list of all 30 kids in the school enrolled in at least one foreign language class. The school offers French, Spanish, and German classes. He knows that 20 kids are in the French class, 18 kids are in the Spanish class, and 10 kids are in the German class. Assuming that 12 kids are enrolled in both French and Spanish, 5 kids in both Spanish and German, and 4 kids in both French and German with 3 kids enrolled in all three classes, what is the probability that by interviewing two random kids he will be able to write about all three classes? Express your answer as a fraction in simplest form.

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