
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 the plane, $n$ points with distinct x-coordinates are marked. A parabola representing the graph of a quadratic polynomial with a leading coefficient of one is drawn through each pair of points. A parabola is called "good" if there are no marked points on or above it, except for the two points through which it is drawn. What is the maximum number of "good" parabolas that could be obtained?

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