
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]


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During a teacher-student interaction meeting, the participants were some subject teachers and students of the class, totaling 31 people. At the meeting, the first teacher exchanged ideas with 16 students; the second teacher with 17 students; the third teacher with 18 students; and so on, until the last teacher exchanged ideas with all students. How many teachers and students attended this meeting?

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