
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 similar triangular array to the previous example, but modify the outer numbers starting from 1 instead of 0, and continuing as 2, 3, 4, ... along the sides. The interior numbers are obtained by adding two adjacent numbers from the previous row. Given the triangular structure:
\[
\begin{array}{ccccccccccc}
& & & & & 1 & & & & & \\
& & & & 2 & & 2 & & & & \\
& & & 3 & & 4 & & 3 & & & \\
& & 4 & & 7 & & 7 & & 4 & & \\
& 5 & & 11 & & 12 & & 11 & & 5 & \\
6 & & 16 & & 23 & & 23 & & 16 & & 6
\end{array}
\]
Calculate the sum of the numbers in the 100th row using exponential notation.

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