
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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A test consists of four single-choice questions, each question having three options A, B, and C. Several students take the test. After grading, it was found that for any group of three students, there is always one question for which their answers are all different, and each student answers all questions. What is the maximum number of students that could have taken the test?

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