
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
Find the smallest natural number  $n$  that the following statement holds :
Let  $A$  be a finite subset of  $\mathbb R^{2}$ . For each  $n$  points in  $A$  there are two lines including these  $n$  points. All of the points lie on two lines.

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