
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 checkerboard has $15$ rows and $20$ columns, with numbers written in each square starting from the upper left corner. The first row is numbered $1,2,\ldots,20$, the second row $21,22,\ldots,40$, and so on. If the board is renumbered so that the left column, top to bottom, is $1,2,\ldots,15,$ the second column $16,17,\ldots,30$ and so on across the board, calculate the sum of the numbers in these squares where numbers are the same in both numbering systems.

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