
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 6 students, each of whom owns books that are not the same as the others, but every two students have exactly one book in common, and each book is owned by exactly two students. How many different books do these 6 students have in total?

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