
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 chessboard has 13 rows and 17 columns. Each small square contains a number, starting from the top-left corner. The first row is filled sequentially with $1, 2, \cdots, 17$; the second row with $18, 19, \cdots, 34$, and so on, until the last row. Now, the numbers are rewritten starting from the top-left corner. The first column is filled sequentially from top to bottom with $1, 2, \cdots, 13$; the second column with $14, 15, \cdots, 26$, and so on, until the last column.
Some of the small squares will have the same number in both the original and the rewritten grid. Find the sum of all such numbers.

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