
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
Consider a volleyball net with sides 10 and 20, divided into $10 \times 20$ square cells, where each cell is further divided into four triangular cells by its diagonals: the vertices of the cell are connected to the center of the cell with strings. The nodes of the net are the vertices and centers of the cells. What is the maximum number of strings connecting neighboring nodes that can be cut so that the net does not fall apart into separate pieces?

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