
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 $T_n$ be the sum of all products $jk$, where $j$ and $k$ are integers and $1\leq j<k\leq n$. This sum $T_n$ is given by $T_n = \frac{(n-1)n(n+1)(3n+2)}{24}$. What is the sum of the 10 smallest values of $n$ such that $T_n$ is divisible by $5$?
A) 225
B) 230
C) 235
D) 240
E) 245

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