
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
Let natural  $n \ge 2$  be given. Let Laura be a student in a class of more than  $n+2$  students, all of which participated in an olympiad and solved some problems. Additionally, it is known that:


- for every pair of students there is exactly one problem that was solved by both students;
- for every pair of problems there is exactly one student who solved both of them;
- one specific problem was solved by Laura and exactly  $n$  other students.

Determine the number of students in Laura's class.

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