
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
At a school, there are three clubs: mathematics, physics, and computer science. The principal observed that among the participants of the mathematics club, exactly $1 / 6$ also attend the physics club, and $1 / 8$ also attend the computer science club. Among the participants of the physics club, exactly $1 / 3$ also attend the mathematics club, and exactly $1 / 5$ attend the computer science club. Finally, among the participants of the computer science club, exactly $1 / 7$ attend the mathematics club. What fraction of the participants of the computer science club attend the physics club?

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