
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
Consider a modified triangular array of numbers where alongside each number being the sum of two adjacent numbers from the previous row as before, each number also has `n`, which is the number of the row, added to it (excluding the first row). The triangular array begins as follows:
\[
\begin{array}{ccccccccccc}
& & & & & 0 & & & & & \\
& & & & 1 & & 1 & & & & \\
& & & 3 & & 3 & & 3 & & & \\
& & 6 & & 7 & & 7 & & 6 & & \\
& 10 & & 14 & & 15 & & 14 & & 10 & \\
15 & & 25 & & 30 & & 30 & & 25 & & 15
\end{array}
\]
Find the sum of the numbers in the 100th row using this modified rule.

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