
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 all positive integers $n$ less than $3000$, let 
$$
a_n =\left\{ 
\begin{array}{lr} 
15, & \text{if } n \text{ is divisible by } 15 \text{ and } 16;\\ 
16, & \text{if } n \text{ is divisible by } 16 \text{ and } 18;\\ 
17, & \text{if } n \text{ is divisible by } 17 \text{ and } 18;\\ 
0, & \text{otherwise}. 
\end{array} 
\right.
$$
Calculate $\sum_{n=1}^{2999} a_n$.
A) 642
B) 653
C) 665
D) 678

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