
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 each integer \( n \geq 2 \), let \( S_n \) be the sum of all products \( jk \), where \( j \) and \( k \) are integers and \( 1 \leq j < k \leq n \). Find the sum of the 10 smallest values of \( n \) such that \( S_n \) is divisible by 5.
A) 275
B) 280
C) 285
D) 290
E) 295

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