
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 $12$ rows and $16$ columns has a number written in each square. In the first numbering system, numbers are written row-wise starting from the upper left corner. In the second system, the board is renumbered column-wise from the top left corner. Some squares have the same numbers under both numbering systems. Find the sum of the numbers in these squares.
A) 344
B) 354
C) 364
D) 374

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