
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
When multiplying two positive numbers, one of which is 75 more than the other, an error resulted in a product that was 1000 less than the true product. Consequently, when dividing (during verification) the incorrect product by the smaller of the factors, the quotient was 227 and the remainder was 113. Find both numbers.

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