
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 plane, there is an open non-self-intersecting polyline with 31 segments (consecutive segments do not lie on the same line). A line containing each segment was drawn through each one. This created 31 lines, some of which may coincide. What is the minimum number of distinct lines that could have been created?

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