
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 350 numbers, with each number at least 5 and at most 150. The sum of the numbers is 38,500. 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. Find the value of $G - L$.

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