
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 where each number is obtained similarly by summing two adjacent numbers from the previous row, but now, the numbers on the sides start from 0 and increase by 2, i.e., 0, 2, 4, ..., etc. Calculate the sum of the numbers in the 50th row, assuming each row's sum follows the recursion pattern $f(n) = 2f(n-1) + 4$ with $f(1)=0$.

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