
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
Take a $2n$-digit number, and consider the first $n$ digits and the last $n$ digits as two separate $n$-digit numbers. 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, $(30+25)^{2}=3025$, so 3025 is a Kabulek number. What are the Kabulek numbers among four-digit numbers?

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