
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
Lara is conducting a survey on students' foreign language preferences for a university newsletter. The university offers French, Spanish, and German courses. Lara has a list of 40 students who are enrolled in at least one of these language courses. She identifies that 28 students are enrolled in the French course, 26 are in the Spanish course, and 15 are in the German course. She also gathered that 10 students are enrolled in both French and Spanish, 6 in both French and German, and 8 in both Spanish and German, while 3 students are studying all three languages. If Lara chooses two students at random from her list, what is the probability that the two selected students represent different language classes? Express your answer as a fraction in simplest form.

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