
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 
\[
b_n =
\begin{cases} 
15, & \text{if } n \text{ is divisible by both } 17 \text{ and } 19; \\
18, & \text{if } n \text{ is divisible by both } 19 \text{ and } 13; \\
17, & \text{if } n \text{ is divisible by both } 13 \text{ and } 17; \\
0, & \text{otherwise}.
\end{cases}
\]
Calculate \( \sum_{n=1}^{2999} b_n \).
A) 448
B) 570
C) 572
D) 574
E) 580

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