
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 the triangular array of numbers with 0, 1, 2, 3, $\dots$ along the sides and interior numbers obtained by adding the two adjacent numbers in the previous row with an extra 1 added to each sum. Rows 1 through 5 are shown.

\[
\begin{array}{ccccccccccc}
& & & & & 0 & & & & & \\
& & & & 1 & & 1 & & & & \\
& & & 2 & & 3 & & 2 & & & \\
& & 3 & & 6 & & 6 & & 3 & & \\
& 4 & & 10 & & 13 & & 10 & & 4 & \\
\end{array}
\]
Find the sum of the numbers in the 100th row. Your answer should use exponential notation, in simplest form.

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