
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  $ 200$  numbers that are each at least  $ 10$  and at most  $ 100$ .  The sum of the numbers is  $ 10{,}000$ .  Let  $ L$  be the *least* possible value of the  $ 50$ th term and let  $ G$  be the *greatest* possible value of the  $ 50$ th term.  What is the value of  $ G \minus{} L$ ?

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