
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
The "Changfei Class" at Hua Shi No.1 consists of $m$ students, and the school specially arranges $n$ teachers as mentors. In one activity of the class, each pair of students asks each other one question, each student asks each mentor one question, and each mentor asks the whole class one question. All the questions asked are different, and there are a total of 51 questions. Find the sum of $m$ and $n$.

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