
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
Consider a $2n$-digit number where the first $n$ digits and the last $n$ digits are each treated as an $n$-digit number. If the square of the sum of these two $n$-digit numbers equals the original $2n$-digit number, then this $2n$-digit number is called a Kabulek number. For example, since $(30 + 25)^2 = 3025$, 3025 is a Kabulek number. Find all Kabulek numbers among the four-digit numbers.

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