
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
Mark starts with a positive integer $N$ and generates a sequence of numbers by subtracting the largest possible perfect square less than or equal to the current number until he reaches zero. If Mark starts with $N = 30$, he gets the following sequence:
\[30, 5, 2, 1, 0\]
The smallest initial integer $M$ for which the sequence generated by this method consists of $10$ numbers, including $M$ and $0$, has what units digit?
A) 2
B) 4
C) 6
D) 8
E) 0

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