
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
There are 40 students in a class. Of these, 22 are involved in physical education clubs, 16 in a mathematics club, and 20 in artistic performance clubs. Additionally, 8 students are involved in both physical education and mathematics clubs, 6 in both artistic performance and mathematics clubs, 10 in both physical education and artistic performance clubs, and 2 in physical education, artistic performance, and mathematics clubs. How many students participate in only one club? How many do not participate in any clubs at all?

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