
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
Roman likes magic and mathematics. Recently, he worked with three-digit or four-digit numbers as follows:

- From a given number, he created two new numbers by splitting it between the hundreds and tens place (e.g., from the number 581, he would get 5 and 81),
- He added the new numbers and recorded the result (in the example given, he would get 86),
- He subtracted the smaller new number from the larger one and recorded the result after the previous sum, thus creating the final number (in the example given, he would get 8676).

For which numbers could Roman have created a) 171, b) 1513? Determine all possibilities.

What is the largest number that can be created this way and from which numbers can it originate? Determine all possibilities.

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