
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
Given 2020 points in the plane, no three of which are collinear, demonstrate that it is possible to construct 505 pairwise disjoint quadrilaterals, not necessarily convex, with vertices among the given points.

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