
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
For each positive integer $n$, let $g(2n)$ denote the units digit of the sum $2 + 4 + 6 + \dots + 2n$. For example, when $n = 1$, $g(2)$ denotes the units digit of $2$, so $g(2) = 2$; when $n = 2$, $g(4)$ denotes the units digit of $2 + 4$, so $g(4) = 6$; when $n = 4$, $g(8)$ denotes the units digit of $2 + 4 + 6 + 8$, so $g(8) = 0$. Find the value of $g(2) + g(4) + g(6) + \dots + g(2022)$.

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