
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
A math interest group at a school is composed of $m$ students, and the school has specifically assigned $n$ teachers as advisors. During one of the group's activities, each pair of students posed a question to each other, each student posed a question to each teacher, and each teacher posed a question to the entire group. All of these questions are unique, totaling 51 questions. Find the values of $m$ and $n$.

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