
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
In an $n \times n$ matrix $\begin{pmatrix} 1 & 2 & 3 & … & n-2 & n-1 & n \\ 2 & 3 & 4 & … & n-1 & n & 1 \\ 3 & 4 & 5 & … & n & 1 & 2 \\ … & … & … & … & … & … & … \\ n & 1 & 2 & … & n-3 & n-2 & n-1\\end{pmatrix}$, if the number at the $i$-th row and $j$-th column is denoted as $a_{ij}(i,j=1,2,…,n)$, then the sum of all $a_{ij}$ that satisfy $2i < j$ when $n=9$ is _____ .

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