
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 
\[
a_n =\left\{ 
\begin{array}{lr} 
15, & \text{if } n \text{ is divisible by } 15 \text{ and } 20;\\ 
20, & \text{if } n \text{ is divisible by } 20 \text{ and } 18;\\ 
18, & \text{if } n \text{ is divisible by } 18 \text{ and } 15;\\ 
0, & \text{otherwise}. 
\end{array} 
\right.
\]
Calculate \(\sum_{n=1}^{2999} a_n\).
A) 1545
B) 1649
C) 1753
D) 1857

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