
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
On a sheet of paper, there are 11 horizontal and 11 vertical lines. The intersection points of these lines are called nodes. A "segment" is defined as a portion of the line connecting two adjacent nodes on the same line. What is the minimum number of segments that must be erased so that no node has more than three segments meeting at it?

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