
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 such that $1 \leq j < k \leq n$. Find the sum of the 10 smallest values of $n$ so that $T_n$ is divisible by 5.

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