
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
Given the set $\{1,2,3,...,n\}(n\geqslant 3)$, let $T\_n$ be the sum of the products of every pair of distinct numbers in the set. For example: $T\_3=1\times2+1\times3+2\times3=\frac{1}{2}[6^2-(1^2+2^2+3^2)]=11$; $T\_4=1\times2+1\times3+1\times4+2\times3+2\times4+3\times4=\frac{1}{2}[10^2-(1^2+2^2+3^2+4^2)]=35$; $T\_5=1\times2+1\times3+1\times4+1\times5+...+3\times5+4\times5=\frac{1}{2}[15^2-(1^2+2^2+3^2+4^2+5^2)]=85$.

Find $T\_8=$_______ (write out the calculation result)

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