
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
An arithmetic sequence consists of $150$ numbers that are each at least $20$ and at most $120$. The sum of the numbers is $12,000$. Let $M$ be the maximum possible value of the median (the $75$th term), and let $m$ be the minimum possible value of this median term. What is $M - m$?

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