
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
At a school with 2500 students, each student studies either Italian or German, and some study both languages. The number who study Italian is between 70% and 75% of the student population, while the number who study German is between 35% and 45%. Determine the difference between the maximum and minimum number of students who could study both languages.

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