
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
A school has $2500$ students, with each studying either Mathematics or Science, and some study both. The number of students studying Mathematics is between $75\%$ and $80\%$ of the student body, while those studying Science are between $35\%$ and $45\%$. Let $m$ be the smallest number of students who could possibly be studying both subjects, and let $M$ be the largest number. Calculate $M - m$.

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