
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 of $15$ rows and $20$ columns is organized with numbers in consecutive order from left to right and top to bottom beginning in the upper left corner, giving the first row numbers $1,2,\ldots,20$, the second row $21,22,\ldots,40$, and so on. 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 continues this pattern across the board. Identify all squares where the numbers remain the same in both numbering systems and find the sum of these numbers.
A) 191  
B) 200  
C) 210  
D) 220  
E) 230

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