
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. Each student studies either Chemistry or Physics, and some students study both. The number of students who study Chemistry is between $50\%$ and $60\%$ of the total student population, and the number who study Physics is between $25\%$ and $35\%$. Let $n$ be the smallest number of students who could study both subjects, and let $N$ be the largest number of students who could study both subjects. Find $N-n$.

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