
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
What is the smallest square of an integer that ends with the longest sequence of the same digits?

For example, if the longest sequence of the same digits were five, then a suitable number would be 24677777 (of course, if it were the smallest square, but it is not). Zero is not considered an acceptable digit.

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