
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 \( 300 \) numbers, each at least \( 20 \) and at most \( 150 \). The sum of the numbers is \( 22{,}500 \). Let \( L \) be the least possible value of the \( 100 \)th term and let \( G \) be the greatest possible value of the \( 100 \)th term. What is the value of \( G - L \)?

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