
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
Each of the $2500$ students in a university studies either German or Italian, or both. The number who study German is between $70\%$ and $75\%$ of the student population, and the number who study Italian is between $35\%$ and $45\%$. Let $m'$ be the smallest number of students who could study both languages, and let $M'$ be the largest number of students who could study both languages. Find $M' - m'$.

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