
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 university has $3000$ students, each studying either History or Psychology, and some study both. The number of students studying History is between $70\%$ and $75\%$ of the university population, and the number studying Psychology is between $40\%$ and $50\%$. Let $m'$ be the smallest number of students who could study both subjects, and let $M'$ be the largest number of students who could study both subjects. Find $M'-m'$.

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