
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 Teacher's Day at a certain school, there are 200 teachers who each send a greeting message to exactly one other teacher. Determine the minimum value of \( k \) such that it is possible to select at least \( k \) representatives to attend a recognition ceremony, where no one in this group has sent a message to anyone else in the group.

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