
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 university, there are $3000$ students enrolled in language courses. Each student studies either German or Russian, and some study both. The number of students who study German is between $70\%$ and $75\%$ of the total student population, and the number studying Russian ranges from $40\%$ to $50\%$. 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. Calculate $M-m$.

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