
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
We know that the last two digits of \(12^{2} = 144\) are both 4, and the last three digits of \(38^{2} = 1444\) are all 4. For a natural number whose unit digit is not zero, what is the maximum number of identical digits that can appear at the end of its square?

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