
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
Among 100 students in a certain school, there are 63 basketball enthusiasts and 75 soccer enthusiasts. However, not every student must have both hobbies. What are the minimum and maximum numbers of students who like both basketball and soccer?

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