
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 necessarily has both hobbies. Find the minimum and maximum number of students who are enthusiasts of both basketball and soccer.

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