
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 links (adjacent links do not lie on the same line). A line containing each link was drawn through every link. A total of 31 lines were obtained, some of which may coincide. What is the minimum number of distinct lines that could be obtained?

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