
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
During the past summer, 100 graduates from the city of $N$ applied to 5 different universities in our country. It turned out that during the first and second waves, each university was unable to reach exactly half of the applicants to that university. In addition, representatives of at least three universities were unable to reach those graduates. What is the maximum number of graduates from the city of $N$ who could have been of interest to the military recruitment office?

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