
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 starting with 0, 1, 2, 3, $\dots$ along the sides. The interior numbers are formed by adding two adjacent numbers in the previous row, but now add 1 to each of the first and last numbers in the row to get the next row. Find the sum of the numbers in the 100th row of this modified array. Express your answer using exponential notation, in simplest form.

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