
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
Consider the supporting line for the set of marked points, i.e., a line such that all marked points lie on one side of this line, and at least one marked point lies on the line itself. This point can be taken as point $A$.

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