
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 $n \geq 4$, let $T_n$ be the sum of all products \(jk\), where \(j\) and \(k\) are integers and \(1 \leq j < k \leq n\). Determine the sum of the 10 smallest values of \(n\) such that \(T_n\) is divisible by 5.
A) 80
B) 82
C) 85
D) 88
E) 90

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