
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
Three students wrote two-digit numbers on the board, each of which is a perfect square. It turned out that if you "glue" them together into one six-digit number, it also turns out to be a perfect square of a natural number. Find all such six-digit numbers.

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