
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 17 rows and 13 columns is numbered as follows: if we number row-wise as $1, 2, \ldots, 13$ in the first row, then $14, 15, \ldots, 26$ in the second row, continuing this pattern to the end. When renumbered column-wise, the first column (top to bottom) is numbered $1, 2, \ldots, 17$, continuing with the next column as $18, 19, \ldots, 34$, and so on. Determine the sum of the numbers in the squares where the two numbering systems agree.
A) 151
B) 161
C) 171
D) 181
E) 191

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