
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
In the nodes of a grid, numbers \( 0, 1, 2, 3 \ldots \) are placed in a spiral. Then, in the center of each cell, the sum of the numbers in its nodes is written (see Fig. 10). Is it true that in the centers of the cells, numbers divisible by 68 will appear infinitely many times? Is it true that in the centers of the cells, the numbers do not repeat?

![Spiral Numbers](https://cdn.mathpix.com/cropped/2024_05_06_57b8ad17478f0226d916g-07.jpg?height=337&width=348&top_left_y=1134&top_left_x=908)


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