
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
A four-digit number has the following property: dividing this four-digit number by its last two digits results in a perfect square (if the tens digit is zero, then only the units digit is used for division), and this perfect square is exactly the square of the sum of the first two digits plus 1. For example, $4802 \div 2 = 2401 = 49^2 = (48 + 1)^2$. What is the smallest four-digit number with the above property?

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