
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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In a school six different courses are taught: mathematics, physics, biology, music, history, geography. The students were required to rank these courses according to their preferences, where equal preferences were allowed. It turned out that:



- **(i)** mathematics was ranked among the most preferred courses by all students;
- **(ii)** no student ranked music among the least preferred ones;
- **(iii)**all students preferred history to geography and physics to biology; and
- **(iv)** no two rankings were the same.


Find the greatest possible value for the number of students in this school.

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