
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
There are \( n + 4 \) labeled points on a plane, where 4 points are the vertices of a square, and the remaining \( n \) points are inside this square. A line segment can be drawn between any two labeled points, but these segments must not contain any other labeled points except at their endpoints, and no two segments can share any points except at their endpoints. Find the maximum number of such line segments that can be drawn.

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