
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
The 2,019 lockers of the 2,019 students at a school are numbered with the squares of the first 2,019 positive natural numbers. That is, the first locker is numbered $1^{2}=1$, the second locker is numbered $2^{2}=4$, the third locker is numbered $3^{2}=9$, and so on until the last locker, which is numbered $2,019^{2}=4,076,361$.

a) How many digits were used to paint the first hundred lockers?

b) By summing all the locker numbers, what is the units digit of this result?

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