
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
A basketball team named "Lingyun Cup" in a school consists of 12 students from 10 classes in grades 10 and 11. Among them, 2 students are from class 3 in grade 10 and class 3 in grade 11 respectively, and 1 student from each of the other classes. The team needs to select 6 main players. What is the probability that these 6 main players come from different classes?

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