
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 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 plus an additional 2 for each pair added. Rows 1 through 6 would look differently due to this change. Calculate the sum of the numbers in the 100th row of this modified array. Assume that for the new base case, the sum in the first row is 2.

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