
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 a math class, the teacher gave the students 2 questions. Scoring is as follows: getting one question correct earns 10 points, partially correct earns 5 points, and completely wrong or unanswered earns 0 points. After grading, the teacher found that there were students with each possible score, and for each score, there were 5 students who had exactly the same score distribution for both questions. How many students are in this class?

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