
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
Let's create a new sequence with the same rules, but we're now looking for a sequence of $9$ numbers including the number $N$ and $0$, not $8$ as in the previous one. What is the smallest number $N$ for which the pattern results in $9$ numbers, and what is the unit digit of $N$?
A) 1
B) 3
C) 5
D) 7
E) 9

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