
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
Sam adds all the positive integers from 1 to 100. Alex does a comparable task, but he rounds each integer to its nearest multiple of 20 before summing. Calculate the positive difference between Sam’s sum and Alex’s sum.

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