
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 23 columns has a number written in each square, beginning in the upper left corner, so that the first row is numbered $1, 2, \ldots, 23$, the second row from $24, 25, \ldots, 46$, continuing this pattern. The board is renumbered such that the first column from top to bottom is $1, 2, \ldots, 15$, the second column from $16, 17, \ldots, 30$, and so on across the board. Find the sum of the numbers in the squares that remain unchanged in both numbering systems.

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