
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
There is a pair of four-digit numbers (2025, 3136) with the following characteristics: each number is a perfect square, and each digit of the second four-digit number is exactly 1 greater than the corresponding digit of the first four-digit number. Find all pairs of five-digit numbers that satisfy these characteristics. (If a pair of five-digit numbers is found, denote them as $(a, b)$).

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