
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
Arrange the terms of the sequence $\{a_{n}\}$ into the following table:<br/>$a_{1}$<br/>$a_{2}$,$a_{3}$<br/>$a_{4}$,$a_{5}$,$a_{6}$,$a_{7}$<br/>$a_{8}$,$a_{9}$,$a_{10}$,$a_{11}$,$a_{12}$,$a_{13}$,$a_{14}$,$a_{15}$<br/>$\ldots $<br/>It is known that the first terms of each row $a_{1}$,$a_{2}$,$a_{4}$,$a_{8}$,$\ldots $ form a sequence $\{b_{n}\}$, $b_{2}=3$ and the sum of the first $n$ terms $S_{n}$ of $\{b_{n}\}$ satisfies $S_{n+1}+S_{n-1}=2S_{n}+2(n\in N*$ and $n\geqslant 2)$. Starting from the third row, the numbers in each row form an arithmetic sequence from left to right, with a common difference. If $a_{130}=19$, then the sum of all terms in the $6$th row is ____.

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