
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 every positive integer $n$ less than $3000$, define
\[
a_n = \left\{\begin{array}{lr}
15, & \text{if } n \text{ is divisible by } 15 \text{ and } 16; \\
16, & \text{if } n \text{ is divisible by } 16 \text{ and } 17; \\
17, & \text{if } n \text{ is divisible by } 15 \text{ and } 17; \\
0, & \text{otherwise}.
\end{array}\right.
\]
Calculate $\sum_{n=1}^{2999} a_n$.
A) 543
B) 560
C) 600
D) 700

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