
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
Adéla wrote two positive integers on the board and tasked Lukáš and Petr with determining the positive difference of the squares of these two numbers. Lukáš, however, calculated the square of the difference between the two given numbers instead. His result was 4038 less than Petr's, who performed the correct calculation. 

What could be the two numbers Adéla wrote on the board? Determine all possible solutions.

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