
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
A triangular array of numbers begins with a first row consisting of the first 100 even integers: $2, 4, 6, \ldots, 200$. Each subsequent row below the first has one fewer number than the row above, and the number in each position in any row after the top row equals the sum of the two numbers diagonally above it in the row immediately above it. Determine the number of entries in the array that are multiples of $23$.

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