
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 a plane, there is an open non-self-intersecting polygonal chain with 31 segments (adjacent segments do not lie on the same line). A line was drawn through each segment, containing that segment. This resulted in 31 lines, some of which may coincide. What is the minimum number of distinct lines that could result?

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