
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
Given Jim starts with a positive integer $n$ and creates a sequence of numbers, where each successive number is obtained by subtracting the largest possible integer square less than or equal to the current number until zero is reached, find the units digit of the smallest number $N$ for which his sequence has 8 numbers.

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