
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 \( 1001 \), let 
\[
a_n = \left\{
    \begin{array}{lr}
        15, & \text{if } n \text{ is divisible by } 10 \text{ and } 15;\\
        10, & \text{if } n \text{ is divisible by } 15 \text{ and } 12;\\
        12, & \text{if } n \text{ is divisible by } 12 \text{ and } 10;\\
        0, & \text{otherwise}.
    \end{array}
\right.
\]
Calculate \(\sum_{n=1}^{1000} a_n\).
- A) 352
- B) 475
- C) 847
- D) 990
- E) 1500

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