
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
In a number system with base 50, every integer whose last digit is 25 or 26 has a square that ends in the same digit as the base. For instance,

$$
\left({ }^{50)} 25\right)^{2}=12 \cdot 50+25
$$

Is there any other base number system where the last digit of a number and the last digit of its square are the same, and this last digit is neither 0 nor 1?

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