
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
Let $S$ be the sum of all numbers of the form $a/b,$ where $a$ and $b$ are [relatively prime](https://artofproblemsolving.com/wiki/index.php/Relatively_prime) positive [divisors](https://artofproblemsolving.com/wiki/index.php/Divisor) of $1000.$ What is the [greatest integer](https://artofproblemsolving.com/wiki/index.php/Floor_function) that does not exceed $S/10$?

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