
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 $u(n)$ denote the unit digit of a positive integer $n$, for example, $u(23) = 3$. If $a_n = u(n^2) - u(n)$, then calculate the sum of the first $2015$ terms of the sequence $\{a_n\}$.

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