
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
Determine the four-digit number in which the sum of the digits, the sum and difference of the third and fourth digits, and the fourth digit itself are all nonzero perfect squares. Additionally, the two-digit number formed by the first two digits is also a perfect square.

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