
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 school, a cheating and hinting competition was held. It is known that $75\%$ of the students did not attend the competition at all, and the remaining students participated in at least one of the competitions. When summarizing the results, it was found that $10\%$ of those who attended participated in both competitions, and there were $1.5$ times more participants in the hinting competition than in the cheating competition. Find the smallest possible number of students in the school.

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