
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
We are given  $2021$  points on a plane, no three of which are collinear. Among any  $5$  of these points, at least  $4$  lie on the same circle. Is it necessarily true that at least  $2020$  of the points lie on the same circle?


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