
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
Last summer, 100 graduates from the city of $N$ applied to 5 different universities in our country. It turned out that each university was unable to reach exactly half of the applicants to that university during the first and second waves. Given that each of the three universities was unable to reach a certain group of graduates, what is the maximum number of graduates from the city of $N$ that could have interested the military enlistment office?

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