
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 sports club has 80 members and three departments: soccer, swimming, and chess. It is known that:

a) There is no athlete who plays chess but does not swim;

b) Soccer players who do not swim all play chess;

c) The chess and soccer departments together have as many members as the swimming department;

d) Every member participates in at least two departments.

How many members belong to all three departments simultaneously?

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