
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
In the morning,  $100$  students study as  $50$  groups with two students in each group. In the afternoon, they study again as  $50$  groups with two students in each group. Determine the largest possible value of  $n$  if  $n$  students can be found such that no two of them study together.

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